@article{sun2019extrapolated,
  title={Extrapolated full waveform inversion with deep learning},
  author={Sun, Hongyu and Demanet, Laurent},
  journal={arXiv preprint arXiv:1909.11536},
  year={2019}
}

@article{araya2019deep,
	title={Deep learning-driven velocity model building workflow},
	author={Araya-Polo, Mauricio and Farris, Stuart and Florez, Manuel},
	journal={The Leading Edge},
	volume={38},
	number={11},
	pages={872a1--872a9},
	year={2019},
	publisher={Society of Exploration Geophysicists}
}

@incollection{araya2020fast,
	title={Fast and Accurate Seismic Tomography via Deep Learning},
	author={Araya-Polo, Mauricio and Adler, Amir and Farris, Stuart and Jennings, Joseph},
	booktitle={Deep Learning: Algorithms and Applications},
	pages={129--156},
	year={2020},
	publisher={Springer}
}

@inproceedings{farris2018tomography,
	title={Tomography: a deep learning vs full-waveform inversion comparison},
	author={Farris, S and Araya-Polo, M and Jennings, J and Clapp, B and Biondi, B},
	booktitle={First EAGE Workshop on High Performance Computing for Upstream in Latin America},
	volume={2018},
	number={1},
	pages={1--5},
	year={2018},
	organization={European Association of Geoscientists \& Engineers}
}

@book{fehler2011seam,
	title={SEAM phase 1: Challenges of subsalt imaging in tertiary basins, with emphasis on deepwater Gulf of Mexico},
	author={Fehler, Michael and Keliher, P Joseph},
	year={2011},
	publisher={Society of Exploration Geophysicists}
}


@article{simonyan2014very,
	title={Very deep convolutional networks for large-scale image recognition},
	author={Simonyan, Karen and Zisserman, Andrew},
	journal={arXiv preprint arXiv:1409.1556},
	year={2014}
}

@inproceedings{krizhevsky2012imagenet,
	title={Imagenet classification with deep convolutional neural networks},
	author={Krizhevsky, Alex and Sutskever, Ilya and Hinton, Geoffrey E},
	booktitle={Advances in neural information processing systems},
	pages={1097--1105},
	year={2012}
}

@misc{clevert2015fast,
	title={Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)},
	author={Djork-Arné Clevert and Thomas Unterthiner and Sepp Hochreiter},
	year={2015},
	eprint={1511.07289},
	archivePrefix={arXiv},
	primaryClass={cs.LG}
}

@article{fomel2013madagascar,
	title={Madagascar: Open-source software project for multidimensional data analysis and reproducible computational experiments},
	author={Fomel, Sergey and Sava, Paul and Vlad, Ioan and Liu, Yang and Bashkardin, Vladimir},
	journal={Journal of Open Research Software},
	volume={1},
	number={1},
	year={2013},
	publisher={Ubiquity Press}
}

@inproceedings{dramsch2019deep,
	title={Deep Learning Application for 4D Pressure Saturation Inversion Compared to Bayesian Inversion on North Sea Data},
	author={Dramsch, Jesper S{\"o}ren and Corte, Gustavo and Amini, Hamed and L{\"u}thje, Mikael and MacBeth, Colin},
	booktitle={Second EAGE Workshop Practical Reservoir Monitoring 2019},
	year={2019}
}

@article{zhang2019regularized,
	author = {Zhendong Zhang  and  Tariq Alkhalifah },
	title = {Regularized elastic full waveform inversion using deep learning},
	journal = {GEOPHYSICS},
	volume = {0},
	number = {ja},
	pages = {1-47},
	year = {2019},
	doi = {10.1190/geo2018-0685.1},
	
	URL = { 
	https://doi.org/10.1190/geo2018-0685.1
	
	},
	eprint = { 
	https://doi.org/10.1190/geo2018-0685.1
	
	}
	,
	abstract = { Obtaining high resolution models of the Earth, especially around the reservoir, is crucial to properly imaging and interpreting the subsurface. We present a regularized elastic full waveform inversion method that uses facies as prior information. Deep neural networks are trained to estimate the distribution of facies in the subsurface. Here, we use facies extracted from wells as the prior information. Seismic data, well logs, and interpreted facies have different resolution and illumination to the subsurface. Besides, a physical process, such as anelasticity in the subsurface, is often too complicated to be fully considered. Therefore, there are often no explicit formulas to connect the data coming from different geophysical surveys. A deep learning method can find the statistically-correct connection without the need to know the complex physics. In our proposed deep learning scheme, we specifically use it to assist the inverse problem instead of the widely used labeling task. We first conduct an adaptive data-selection elastic full waveform inversion using the observed seismic data and obtain estimates of the subsurface, which do not need to be perfect. Then we use extracted facies information from the wells and force the estimated model to fit the facies by training deep neural networks. In this way, a list of facies is mapped to a 2D or 3D inverted model guided mainly by the structure features of the model. The multidimensional distribution of facies is used either as a regularization term or as an initial model for the next waveform inversion. The proposed method has two main features: 1) it applies to any kind of distributions of data samples and 2) it interpolates facies between wells guided by the structure of the estimated models. Results with synthetic and field data illustrate the benefits and limitations of this method. }
}

@article{ivanov2017traveltime,
	title={Traveltime parameters in tilted orthorhombic medium},
	author={Ivanov, Yuriy and Stovas, Alexey},
	journal={Geophysics},
	volume={82},
	number={6},
	pages={C187--C200},
	year={2017},
	publisher={Society of Exploration Geophysicists}
}

@article{kazei2019scattering,
	title={Scattering Radiation Pattern Atlas: What anisotropic elastic properties can body waves resolve?},
	author={Kazei, Vladimir and Alkhalifah, Tariq},
	journal={Journal of Geophysical Research: Solid Earth},
	volume={124},
	number={3},
	pages={2781--2811},
	year={2019},
	publisher={Wiley Online Library}
}

@inproceedings{skopintseva2019regularization,
	title={Regularization in Full Waveform Inversion: OBC vs Streamer Data Results Over a Gas Cloud},
	author={Skopintseva, L and Ravaut, C and Pedersen, {\O} and Maa{\o}, FA and Hartvigsen, KO},
	booktitle={81st EAGE Conference and Exhibition 2019},
	year={2019}
}

@inproceedings{oye2019velocity,
	title={Velocity Model Building from Raw Shot Gathers Using Machine Learning},
	author={{\O}ye, OK and Dahl, EK},
	booktitle={81st EAGE Conference and Exhibition 2019},
	year={2019}
}

@article{richardson2018seismic,
	title={Seismic full-waveform inversion using deep learning tools and techniques},
	author={Richardson, Alan},
	journal={arXiv preprint arXiv:1801.07232},
	year={2018}
}

@incollection{wu2018inversionnet,
	title={InversionNet: Accurate and efficient seismic waveform inversion with convolutional neural networks},
	author={Wu, Yue and Lin, Youzuo and Zhou, Zheng},
	booktitle={SEG Technical Program Expanded Abstracts 2018},
	pages={2096--2100},
	year={2018},
	publisher={Society of Exploration Geophysicists}
}

@article{zhang2018velocitygan,
	title={VelocityGAN: Data-Driven Full-Waveform Inversion Using Conditional Adversarial Networks},
	author={Zhang, Zhongping and Wu, Yue and Lin, Youzuo and Zhou, Zheng},
	journal={arXiv preprint arXiv:1809.10262},
	year={2018}
}

@article{yang2019deep,
	title={Deep-learning inversion: a next generation seismic velocity-model building method},
	author={Yang, Fangshu and Ma, Jianwei},
	journal={Geophysics},
	volume={84},
	number={4},
	pages={1--133},
	year={2019},
	publisher={Society of Exploration Geophysicists}
}

@inproceedings{ovcharenko2019style,
	title={Style transfer for generation of realistically textured subsurface models},
	author={Ovcharenko, Oleg and Kazei, Vladimir and Peter, Daniel and Alkhalifah, Tariq},
	booktitle={SEG Technical Program Expanded Abstracts 2019},
	year={2019},
	publisher={Society of Exploration Geophysicists}
}


@inproceedings{simard2003best,
	title={Best practices for convolutional neural networks applied to visual document analysis.},
	author={Simard, Patrice Y and Steinkraus, David and Platt, John C and others},
	booktitle={Icdar},
	volume={3},
	number={2003},
	year={2003}
}

@article{sun2019robust,
	title={Robust Full-Waveform Inversion with Radon-Domain Matching Filter},
	author={Sun, Bingbing and Alkhalifah, Tariq},
	journal={Geophysics},
	volume={84},
	number={5},
	pages={1--121},
	year={2019},
	publisher={Society of Exploration Geophysicists}
}

@article{dunford2014pareto,
	title={The pareto principle},
	author={Dunford, Rosie and Su, Quanrong and Tamang, Ekraj},
	year={2014},
	publisher={University of Plymouth}
}

@article{scikit-learn,
	title={Scikit-learn: Machine Learning in {P}ython},
	author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
	and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
	and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
	Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
	journal={Journal of Machine Learning Research},
	volume={12},
	pages={2825--2830},
	year={2011}
}

@article{dozat2016incorporating,
	title={Incorporating nesterov momentum into adam},
	author={Dozat, Timothy},
	year={2016}
}

@article{mann1999common,
	title={Common-reflection-surface stack—A real data example},
	author={Mann, J{\"u}rgen and J{\"a}ger, Rainer and M{\"u}ller, Thilo and H{\"o}cht, German and Hubral, Peter},
	journal={Journal of applied geophysics},
	volume={42},
	number={3-4},
	pages={301--318},
	year={1999},
	publisher={Elsevier}
}

@article{gelchinsky1999multifocusing,
	title={Multifocusing homeomorphic imaging: Part 1. Basic concepts and formulas},
	author={Gelchinsky, Boris and Berkovitch, Alexander and Keydar, Shmariahu},
	journal={Journal of applied geophysics},
	volume={42},
	number={3-4},
	pages={229--242},
	year={1999},
	publisher={Elsevier}
}

@article{roth1994,
	title = {Neural Networks and Inversion of Seismic Data},
	volume = {99},
	copyright = {Copyright 1994 by the American Geophysical Union.},
	issn = {2156-2202},
	abstract = {Neural networks can be viewed as applications that map one space, the input space, into some output space. In order to simulate the desired mapping the network has to go through a learning process consisting of an iterative change of the internal parameters, through the presentation of many input patterns and their corresponding output patterns. The training process is accomplished if the error between the computed output and the desired output pattern is minimal for all examples in the training set. The network will then simulate the desired mapping on the restricted domain of the training examples. We describe an experiment where a neural network is designed to accept a synthetic common shot gather (i.e., a set of seismograms obtained from a single source), as its input pattern and to compute the corresponding one-dimensional large-scale velocity model as its output. The subsurface models are built up of eight layers with constant layer thickness over a homogeneous half-space, 450 examples are used to train the network. After the training process the network never computes a subsurface model which perfectly fits the desired one, but the approximation of the network is sufficient to take this model as starting model for further seismic imaging algorithms. The trained network computes satisfactory velocity profiles for 80\% of the new seismic gathers not included in the training set. Although the network gives results that are stable when the input is contaminated with white noise, the network is not robust against strong, i.e., correlated, noise. This application proves that neural networks are able to solve nontrivial inverse problems.},
	language = {en},
	number = {B4},
	journal = {Journal of Geophysical Research: Solid Earth},
	doi = {10.1029/93JB01563},
	author = {R\"oth, Gunter and Tarantola, Albert},
	year = {1994},
	pages = {6753-6768},
	file = {/home/kazeiv/Zotero/storage/KH56Y2XT/Röth and Tarantola - 1994 - Neural networks and inversion of seismic data.pdf;/home/kazeiv/Zotero/storage/FR4DDSN2/93JB01563.html}
}

@article{li2019,
	archivePrefix = {arXiv},
	eprinttype = {arxiv},
	eprint = {1901.07733},
	primaryClass = {cs},
	title = {Deep Learning {{Inversion}} of {{Seismic Data}}},
	abstract = {In this paper, we propose a new method to tackle the mapping challenge from time-series data to spatial image in the field of seismic exploration, i.e., reconstructing the velocity model directly from seismic data by deep neural networks (DNNs). The conventional way to address this ill-posed seismic inversion problem is through iterative algorithms, which suffer from poor nonlinear mapping and strong non-uniqueness. Other attempts may either import human intervention errors or underuse seismic data. The challenge for DNNs mainly lies in the weak spatial correspondence, the uncertain reflection-reception relationship between seismic data and velocity model as well as the time-varying property of seismic data. To approach these challenges, we propose an end-to-end Seismic Inversion Networks (SeisInvNet for short) with novel components to make the best use of all seismic data. Specifically, we start with every seismic trace and enhance it with its neighborhood information, its observation setup and global context of its corresponding seismic profile. Then from enhanced seismic traces, the spatially aligned feature maps can be learned and further concatenated to reconstruct velocity model. In general, we let every seismic trace contribute to the reconstruction of the whole velocity model by finding spatial correspondence. The proposed SeisInvNet consistently produces improvements over the baselines and achieves promising performance on our proposed SeisInv dataset according to various evaluation metrics, and the inversion results are more consistent with the target from the aspects of velocity value, subsurface structure and geological interface. In addition to the superior performance, the mechanism is also carefully discussed, and some potential problems are identified for further study.},
	journal = {arXiv:1901.07733 [cs]},
	author = {Li, Shucai and Liu, Bin and Ren, Yuxiao and Chen, Yangkang and Yang, Senlin and Wang, Yunhai and Jiang, Peng},
	month = jan,
	year = {2019},
	keywords = {Computer Science - Artificial Intelligence,Computer Science - Computer Vision and Pattern Recognition},
	file = {/home/kazeiv/Zotero/storage/T89ZTCB7/Li et al. - 2019 - Deep learning Inversion of Seismic Data.pdf;/home/kazeiv/Zotero/storage/4E5XLMYF/1901.html}
}

@inproceedings{zheng2019,
	title = {Elastic {{Pre}}-Stack {{Seismic Inversion}} in {{Stratified Media Using Machine Learning}}},
	abstract = {The similarity between seismic inversion and machine learning lies in the fact that both are essentially optimization problems. This study describes a workflow in which the pre-stack seismic inversion is framed as a deep learning problem. The earth medium of interest is elastic with weak lateral variations. A convolutional neural network (CNN) is trained and tested on a set of synthetic earth models and seismic records. The trained network is then used to make predictions of subsurface elastic parameters directly from field data from a land survey. The predicted elastic parameters, even in the absence of low frequency content in the input seismic data, show a good match with the well logs. The P-wave velocity model appears to have better resolution and accuracy than the result derived from travel-time tomography. Adequate predictions from the CNN is achieved by the careful construction of training samples and the conditioning of seismic data so that the synthetic data used for training approximately represent the statistics of the geology and field data. The computational efficiency of using deep learning in such a way for waveform inversion may be desirable for elastic model building.},
	language = {English},
	booktitle = {81st {{EAGE Conference}} and {{Exhibition}} 2019},
	doi = {10.3997/2214-4609.201901524},
	author = {Zheng, Y.},
	month = jun,
	year = {2019},
	file = {/home/kazeiv/Zotero/storage/2K8VB8NM/Zheng - 2019 - Elastic Pre-stack Seismic Inversion in Stratified .pdf;/home/kazeiv/Zotero/storage/6FC87LPP/publicationdetails.html}
}

@inproceedings{ruan2018global,
	title={Global Adjoint Tomography-New Generation Earth Mantle Model},
	author={Ruan, Y and Lei, W and Lefebvre, MP and Modrak, R and Smith, JA and Orsvuran, R and Bozdag, E and Chen, Y and Hill, J and Podhorszki, N and others},
	booktitle={AGU Fall Meeting Abstracts},
	year={2018}
}

@article{operto2018role,
	title={On the role of density and attenuation in three-dimensional multiparameter viscoacoustic VTI frequency-domain FWI: an OBC case study from the North Sea},
	author={Operto, S and Miniussi, A},
	journal={Geophysical Journal International},
	volume={213},
	number={3},
	pages={2037--2059},
	year={2018},
	publisher={Oxford University Press}
}

@article{kalita2019regularized,
	title={Regularized full-waveform inversion with automated salt flooding},
	author={Kalita, Mahesh and Kazei, Vladimir and Choi, Yunseok and Alkhalifah, Tariq},
	journal={Geophysics},
	volume={84},
	number={4},
	pages={R569--R582},
	year={2019},
	publisher={Society of Exploration Geophysicists}
}

@inproceedings{kazei2019realistically,
	title={Realistically Textured Random Velocity Models for Deep Learning Applications},
	author={Kazei, V and Ovcharenko, O and Alkhalifah, T and Simons, F},
	booktitle={81st EAGE Conference and Exhibition 2019},
	year={2019}
}


@misc{ovcharenko2019deep,
	author={Ovcharenko, Oleg and Kazei, Vladimir and Kalita, Mahesh and Peter, Daniel and Alkhalifah, Tariq Ali},
	publisher={Society of Exploration Geophysicists},
	title={Deep learning for low-frequency extrapolation from multi-offset seismic data},
	url={http://hdl.handle.net/10754/655680},
	journal={Submitted to Geophysics},
	year={2019}
}

@inproceedings{kazei2017salt,
	title={Salt-body Inversion with Minimum Gradient Support and Sobolev Space Norm Regularizations},
	author={Kazei, V.V. and Kalita, M. and Alkhalifah, T.},
	booktitle={79th EAGE Conference and Exhibition 2017},
	year={2017}
}

@incollection{jin2018learn,
	title={{Learn low wavenumber information in FWI via deep inception based convolutional networks}},
	author={Jin, Yuchen and Hu, Wenyi and Wu, Xuqing and Chen, Jiefu},
	booktitle={SEG Technical Program Expanded Abstracts 2018},
	pages={2091--2095},
	year={2018},
	publisher={Society of Exploration Geophysicists}
}

@article{yao2019extraction,
	title={Extraction of the tomography mode with nonstationary smoothing for full-waveform inversion},
	author={Yao, Gang and da Silva, Nuno V and Kazei, Vladimir and Wu, Di and Yang, Chenhao},
	journal={Geophysics},
	volume={84},
	number={4},
	pages={R527--R537},
	year={2019},
	publisher={Society of Exploration Geophysicists}
}


@article{Olver,
  title = {The {{Asymptotic Expansion}} of {{BEssel Functions}} of {{Large Order}}},
  volume = {247},
  doi = {10.1098/rsta.1954.0021},
  abstract = {New expansions are obtained for the functions I\textsubscript{{$\nu$}}({$\nu$}z), K\textsubscript{{$\nu$}}({$\nu$}z) and their derivatives in terms of elementary functions, and for the functions J\textsubscript{{$\nu$}}({$\nu$}z), Y\textsubscript{{$\nu$}}({$\nu$}z), H\textsubscript{{$\nu$}}{$^{(}^1^{)}$}({$\nu$}z), H\textsubscript{{$\nu$}}{$^{(}^2^{)}$}({$\nu$}z) and their derivatives in terms of Airy functions, which are uniformly valid with respect to z when |{$\nu$}| is large. New series for the zeros and associated values arc derived by reversion and used to determine the distribution of the zeros of functions of large order in the z-plane. Particular attention is paid to the complex zeros of Yₙ(z) and the Hankel functions when the order n is an integer or half an odd integer, and for this purpose some new asymptotic expansions of the Airy functions are derived. Tables are given of complex zeros of Airy functions and other quantities which facilitate the rapid calculation of the smaller complex zeros of Yₙ(z), Yₙ(z), and the Hankel functions and their derivatives, when 2n is an integer, to an accuracy of three or four significant figures.},
  number = {930},
  journal = {Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  author = {Olver, F. W. J.},
  year = {1954},
  pages = {328-368},
  eprint = {http://rsta.royalsocietypublishing.org/content/247/930/328.full.pdf+html}
}

@article{GRL:GRL24084,
  title = {Full Waveform Inversion of Reflection Seismic Data for Ocean Temperature Profiles},
  volume = {35},
  issn = {1944-8007},
  doi = {10.1029/2007GL032359},
  number = {4},
  journal = {Geophysical Research Letters},
  author = {Wood, Warren T. and Holbrook, W. Steven and Sen, Mrinal K. and Stoffa, Paul L.},
  year = {2008},
  keywords = {seismic oceanography,waveform inversion},
  pages = {L04608}
}

@article{woodward:1232,
  title = {Wave-Equation Tomography},
  volume = {7},
  doi = {10.1190/1.1892498},
  number = {1},
  journal = {SEG Technical Program Expanded Abstracts},
  author = {Woodward, Marta Jo and Rocca, Fabio},
  year = {1988},
  pages = {1232-1235},
  publisher = {{SEG}},
  urlx = {http://link.aip.org/link/?SGA/7/1232/1}
}

@article{sirgue2004,
  title = {Efficient Waveform Inversion and Imaging: {{A}} Strategy for Selecting Temporal Frequencies},
  volume = {69},
  doi = {10.1190/1.1649391},
  number = {1},
  journal = {Geophysics},
  author = {Sirgue, L. and Pratt, R.},
  year = {2004},
  pages = {231-248},
  eprint = {http://library.seg.org/doi/pdf/10.1190/1.1649391}
}

@book{brekhovskikh1999acoustics,
  series = {Wave {{Phenomena}}},
  title = {Acoustics of {{Layered Media II}}: {{Point Sources}} and {{Bounded Beams}}},
  isbn = {978-3-540-65592-3},
  publisher = {{Springer}},
  author = {Brekhovskikh, L.M. and Godin, O.A.},
  year = {1999},
  lccn = {99012348}
}

@book{brekhovskikh1998acoustics,
  series = {Wave {{Phenomena}}},
  title = {Acoustics of {{Layered Media I}}: {{Plane}} and {{Quasi}}-{{Plane Waves}}},
  isbn = {978-3-540-64724-9},
  publisher = {{Springer}},
  author = {Brekhovskikh, L. M. and Godin, O. A.},
  year = {1998},
  lccn = {98027950}
}

@article{wolfHead,
  title = {The Amplitude and Character of Refraction Waves},
  volume = {1},
  doi = {10.1190/1.1437117},
  number = {3},
  journal = {Geophysics},
  author = {Wolf, A.},
  year = {1936},
  pages = {319-326},
  publisher = {{SEG}}
}

@article{wolfTrans,
  title = {The Reflection of Elastic Waves from Transition Layers of Variable Velocity},
  volume = {2},
  doi = {10.1190/1.1438104},
  number = {4},
  journal = {Geophysics},
  author = {Wolf, Alfred},
  year = {1937},
  pages = {357-363},
  publisher = {{SEG}}
}

@article{Liner,
  title = {The {{Wolf}} Ramp: {{Reflection}} Characteristics of a Transition Layer},
  volume = {75},
  doi = {10.1190/1.3476312},
  abstract = {The modern use of spectral decomposition has shown that reflection events in practice are always frequency dependent, a phenomenon called reflectivity dispersion. Often, this can be attributed to strong interference effects from neighboring reflection coefficients of the classical type (i.e., parameter discontinuities or jumps). However, an intrinsic frequency dependence from a single layer is possible if the contact is not a jump discontinuity but a gradual transition. We have expanded the normal-incidence theory of a linear velocity transition zone (termed a Wolf ramp) and have shown how it leads to frequency-dependent reflectivity. The development of waveform forward modeling in turn has led to a ramp detection method that we have tested on migrated field data.},
  number = {5},
  journal = {Geophysics},
  author = {Liner, Christopher L. and Bodmann, Bernhard G.},
  year = {2010},
  pages = {A31-A35},
  eprint = {http://geophysics.geoscienceworld.org/content/75/5/A31.full.pdf+html}
}

@book{abramowitzStegun,
  address = {New York},
  edition = {9th Dover printing, 10th GPO printing},
  title = {Handbook of {{Mathematical Functions}} with {{Formulas}}, {{Graphs}}, and {{Mathematical Tables}}},
  publisher = {{Dover}},
  author = {Abramowitz, Milton and Stegun, Irene A.},
  year = {1964}
}

@article{Balogh,
  title = {Asymptotic {{Expansions}} of the {{Modified BEssel Function}} of the {{Third Kind}} of {{Imaginary Order}}},
  volume = {15},
  doi = {10.1137/0115114},
  number = {5},
  journal = {SIAM Journal on Applied Mathematics},
  author = {Balogh, C.},
  year = {1967},
  pages = {1315-1323},
  eprint = {http://epubs.siam.org/doi/pdf/10.1137/0115114}
}

@article{Alexiou,
  title = {Fast Analytic Formulas for the Modified {{BEssel}} Functions of Imaginary Order for Spectral Line Broadening Calculations},
  volume = {62},
  issn = {0022-4073},
  doi = {10.1016/S0022-4073(98)00109-5},
  number = {4},
  journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},
  author = {Poqu\'erusse, A. and Alexiou, S.},
  year = {1999},
  keywords = {Coulomb excitation},
  pages = {389-395}
}

@incollection{zhang2012compensating,
  title = {Compensating for Source and Receiver Ghost Effects in Reverse Time Migration},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2012},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Zhang, Yu and Roberts, Graham and Khalil, Adel},
  year = {2012},
  pages = {1-5},
  doi = {10.1190/segam2012-0626.1}
}

@article{sava2003angle,
  title = {Angle-Domain Common-Image Gathers by Wavefield Continuation Methods},
  volume = {68},
  number = {3},
  journal = {Geophysics},
  author = {Sava, Paul C and Fomel, Sergey},
  year = {2003},
  pages = {1065-1074},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{virieux2009,
  title = {An Overview of Full-Waveform Inversion in Exploration Geophysics},
  volume = {74},
  number = {6},
  journal = {Geophysics},
  author = {Virieux, Jean and Operto, St\'ephane},
  year = {2009},
  pages = {WCC1-WCC26},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{ravaut2004multiscale,
  title = {Multiscale Imaging of Complex Structures from Multifold Wide-Aperture Seismic Data by Frequency-Domain Full-Waveform Tomography: Application to a Thrust Belt},
  volume = {159},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Ravaut, C and Operto, S and Improta, L and Virieux, J and Herrero, A and Dell'Aversana, P},
  year = {2004},
  pages = {1032-1056},
  publisher = {{Oxford University Press}}
}

@article{ewald1969,
  title = {Introduction to the Dynamical Theory of {{X}}-Ray Diffraction},
  volume = {25},
  number = {1},
  journal = {Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography},
  author = {Ewald, PP},
  year = {1969},
  pages = {103-108},
  publisher = {{International Union of Crystallography}}
}

@article{goldstein2000,
  title = {Relative Importance of Near-, Intermediate-and Far-Field Displacement Terms in Layered Earth Synthetic Seismograms},
  volume = {90},
  number = {2},
  journal = {Bulletin of the Seismological Society of America},
  author = {Ichinose, Gene A and Goldstein, Peter and Rodgers, Arthur J},
  year = {2000},
  pages = {531-536},
  publisher = {{Seismological Society of America}}
}

@article{McGrave1998,
  title = {Theory of Nonstationary Linear Filtering in the {{Fourier}} Domain with Application to Time-variant Filtering},
  volume = {63},
  doi = {10.1190/1.1444318},
  number = {1},
  journal = {GEOPHYSICS},
  author = {Margrave, Gary F.},
  year = {1998},
  pages = {244-259},
  eprint = {http://dx.doi.org/10.1190/1.1444318}
}

@article{rutherford1911,
  title = {{{LXXIX}}. {{The}} Scattering of {$\alpha$} and {$\beta$} Particles by Matter and the Structure of the Atom},
  volume = {21},
  doi = {10.1080/14786440508637080},
  number = {125},
  journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
  author = {Rutherford, Ernest},
  year = {1911},
  pages = {669-688},
  publisher = {{Taylor \& Francis}}
}

@article{tessmer2011,
  title = {Using the Rapid Expansion Method for Accurate Time-Stepping in Modeling and Reverse-Time Migration},
  volume = {76},
  doi = {10.1190/1.3587217},
  number = {4},
  journal = {GEOPHYSICS},
  author = {Tessmer, Ekkehart},
  year = {2011},
  pages = {S177-S185},
  eprint = {http://dx.doi.org/10.1190/1.3587217}
}

@article{virieux2011,
  title = {A Review of the Spectral, Pseudo-Spectral, Finite-Difference and Finite-Element Modelling Techniques for Geophysical Imaging},
  volume = {59},
  doi = {10.1111/j.1365-2478.2011.00967.x},
  number = {5},
  journal = {Geophysical Prospecting},
  author = {Virieux, Jean and Calandra, Henri and Plessix, Ren\'e-\'Edouard},
  year = {2011},
  pages = {794-813},
  publisher = {{Wiley Online Library}}
}

@article{leeuwen2013,
  title = {Mitigating Local Minima in Full-Waveform Inversion by Expanding the Search Space},
  volume = {195},
  doi = {10.1093/gji/ggt258},
  abstract = {Wave equation based inversions, such as full-waveform inversion and reverse-time migration, are challenging because of their computational costs, memory requirements and reliance on accurate initial models. To confront these issues, we propose a novel formulation of wave equation based inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term, which measures how accurately the wavefields satisfy the wave equation. This new approach is a major departure from current formulations where forward and adjoint wavefields, which both satisfy the wave equation, are correlated to compute updates for the unknown model parameters. Instead, we carry out the inversions over two alternating steps during which we first estimate the wavefield everywhere, given the current model parameters, source and observed data, followed by a second step during which we update the model parameters, given the estimate for the wavefield everywhere and the source. Because the inversion involves both the synthetic wavefields and the medium parameters, its search space is enlarged so that it suffers less from local minima. Compared to other formulations that extend the search space of wave equation based inversion, our method differs in several aspects, namely (i) it avoids storage and updates of the synthetic wavefields because we calculate these explicitly by finding solutions that obey the wave equation and fit the observed data and (ii) no adjoint wavefields are required to update the model, instead our updates are calculated from these solutions directly, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research.},
  number = {1},
  journal = {Geophysical Journal International},
  author = {{van Leeuwen}, Tristan and Herrmann, Felix J.},
  year = {2013},
  pages = {661-667},
  eprint = {http://gji.oxfordjournals.org/content/195/1/661.full.pdf+html}
}

@article{GPR:GPR12010,
  title = {The Use of Low Frequencies in a Full-Waveform Inversion and Impedance Inversion Land Seismic Case Study},
  volume = {61},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12010},
  number = {4},
  journal = {Geophysical Prospecting},
  author = {Baeten, Guido and {de Maag}, Jan Willem and Plessix, Ren\'e-Edouard and Klaassen, Rini and Qureshi, Tahira and Kleemeyer, Maren and {ten Kroode}, Fons and Rujie, Zhang},
  year = {2013},
  keywords = {Full-waveform inversion,Impedance},
  pages = {701-711},
  publisher = {{Blackwell Publishing Ltd}}
}

@article{Xie01092006,
  title = {Wave-Equation-Based Seismic Illumination Analysis},
  volume = {71},
  doi = {10.1190/1.2227619},
  abstract = {We present a wave-equation-based method for seismic illumination analysis. A one-way wave-equation-based, generalized screen propagator is used to extrapolate the wavefields from sources and receivers to the subsurface target. A local plane-wave analysis is used at the target to calculate localized, directional energy fluxes for both source and receiver wavefields. We construct an illumination matrix using these energy fluxes to quantify the target illumination conditions. The target geometry information is used to manipulate the illumination matrix and generate different types of illumination measures. The wave-equation-based approach can properly handle forward multiple-scattering phenomena, including focusing/defocusing, diffraction, and interference effects. It can be directly applied to complex velocity models. Velocity-model smoothing and Fresnel-zone smoothing are not required. Different illumination measurements derived from this method can be applied to target-oriented or volumetric illumination analyses. This new method is flexible and practical for illumination analysis in complex 2D and 3D velocity models with nontrivial acquisition and target geometries.},
  number = {5},
  journal = {Geophysics},
  author = {Xie, Xiao-Bi and Jin, Shengwen and Wu, Ru-Shan},
  year = {2006},
  pages = {S169-S177},
  eprint = {http://geophysics.geoscienceworld.org/content/71/5/S169.full.pdf+html}
}

@article{LeakingModes,
  title = {Guided Waves in Near-Surface Seismic Surveys},
  volume = {25},
  issn = {1944-8007},
  doi = {10.1029/98GL00549},
  number = {7},
  journal = {Geophysical Research Letters},
  author = {Roth, M. and Holliger, K. and Green, A. G.},
  year = {1998},
  pages = {1071-1074}
}

@article{alkhalifah2014scattering,
  title = {Scattering-Angle Based Filtering of the Waveform Inversion Gradients},
  volume = {200},
  doi = {10.1093/gji/ggu379},
  abstract = {Full waveform inversion (FWI) requires a hierarchical approach to maneuver the complex non-linearity associated with the problem of velocity update. In anisotropic media, the non-linearity becomes far more complex with the potential trade-off between the multiparameter description of the model. A gradient filter helps us in accessing the parts of the gradient that are suitable to combat the potential non-linearity and parameter trade-off. The filter is based on representing the gradient in the time-lag normalized domain, in which the low scattering angle of the gradient update is initially muted out in the FWI implementation, in what we may refer to as a scattering angle continuation process. The result is a low wavelength update dominated by the transmission part of the update gradient. In this case, even 10 Hz data can produce vertically near-zero wavenumber updates suitable for a background correction of the model. Relaxing the filtering at a later stage in the FWI implementation allows for smaller scattering angles to contribute higher-resolution information to the model. The benefits of the extended domain based filtering of the gradient is not only it's ability in providing low wavenumber gradients guided by the scattering angle, but also in its potential to provide gradients free of unphysical energy that may correspond to unrealistic scattering angles.},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Alkhalifah, Tariq},
  year = {2015},
  pages = {363-373},
  eprint = {http://gji.oxfordjournals.org/content/200/1/363.full.pdf+html}
}

@article{tarantola1984,
  title = {Inversion of Seismic Reflection Data in the Acoustic Approximation},
  volume = {49},
  number = {8},
  journal = {Geophysics},
  author = {Tarantola, Albert},
  year = {1984},
  pages = {1259-1266},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{marmousi1991,
  title = {Marmousi, Model and Data},
  journal = {The Marmousi Experience},
  author = {Bourgeois, A and Bourget, M and Lailly, P and Poulet, M and Ricarte, P and Versteeg, R},
  year = {1991},
  pages = {5-16},
  publisher = {{Eur. Ass. Expl. Geophys}}
}

@article{biondi2013,
  title = {Tomographic Full-Waveform Inversion ({{TFWI}}) by Combining {{FWI}} and Wave-Equation Migration Velocity Analysis},
  volume = {32},
  doi = {10.1190/tle32091074.1},
  number = {9},
  journal = {The Leading Edge},
  author = {Biondi, Biondo and Almomin, Ali},
  year = {2013},
  pages = {1074-1080},
  eprint = {http://dx.doi.org/10.1190/tle32091074.1}
}

@article{bozdag2011,
  title = {Misfit Functions for Full Waveform Inversion Based on Instantaneous Phase and Envelope Measurements},
  volume = {185},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Bozd{\u a}g, Ebru and Trampert, Jeannot and Tromp, Jeroen},
  year = {2011},
  pages = {845-870},
  publisher = {{Oxford University Press}}
}

@article{wu2014,
  title = {Seismic Envelope Inversion and Modulation Signal Model},
  volume = {79},
  doi = {10.1190/geo2013-0294.1},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Wu, Ru-Shan and Luo, Jingrui and Wu, Bangyu},
  year = {2014},
  pages = {WA13-WA24},
  eprint = {http://dx.doi.org/10.1190/geo2013-0294.1}
}

@article{wim2010,
  title = {A Correlation-Based Misfit Criterion for Wave-Equation Traveltime Tomography},
  volume = {182},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.2010.04681.x},
  abstract = {Wave-equation traveltime tomography tries to obtain a subsurface velocity model from seismic data, either passive or active, that explains their traveltimes. A key step is the extraction of traveltime differences, or relative phase shifts, between observed and modelled finite-frequency waveforms. A standard approach involves a correlation of the observed and measured waveforms. When the amplitude spectra of the waveforms are identical, the maximum of the correlation is indicative of the relative phase shift. When the amplitude spectra are not identical, however, this argument is no longer valid. We propose an alternative criterion to measure the relative phase shift. This misfit criterion is a weighted norm of the correlation and is less sensitive to differences in the amplitude spectra. For practical application it is important to use a sensitivity kernel that is consistent with the way the misfit is measured. We derive this sensitivity kernel and show how it differs from the standard banana\dbend{}doughnut sensitivity kernel. We illustrate the approach on a cross-well data set.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Van Leeuwen, T. and Mulder, W. A.},
  year = {2010},
  keywords = {Body waves,Inverse theory,Seismic tomography},
  pages = {1383-1394},
  publisher = {{Blackwell Publishing Ltd}}
}

@article{nocedal1980,
  title = {Updating Quasi-{{Newton}} Matrices with Limited Storage},
  volume = {35},
  number = {151},
  journal = {Mathematics of computation},
  author = {Nocedal, Jorge},
  year = {1980},
  pages = {773-782}
}

@article{kazei2015TS,
  title = {Pseudo-Spectral Full-Waveform Inversion},
  number = {2},
  journal = {Seismic Technologies},
  author = {Kazei, VV and Kashtan, BM and Troyan, VN and Tessmer, Ekkehart},
  year = {2015},
  pages = {18-28}
}

@article{luo1991wave,
  title = {Wave-Equation Traveltime Inversion},
  volume = {56},
  number = {5},
  journal = {Geophysics},
  author = {Luo, Yi and Schuster, Gerard T},
  year = {1991},
  pages = {645-653},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{broad2007,
  title = {Modeling the Impact of Wide-Azimuth Acquisition on Subsalt Imaging},
  volume = {72},
  doi = {10.1190/1.2736516},
  number = {5},
  journal = {GEOPHYSICS},
  author = {VerWest, Bruce J. and Lin, Dechun},
  year = {2007},
  pages = {SM241-SM250},
  eprint = {http://dx.doi.org/10.1190/1.2736516}
}

@article{dai2014uncertainty,
  title = {Uncertainty Quantification for {{CO2}} Sequestration and Enhanced Oil Recovery},
  volume = {63},
  journal = {Energy Procedia},
  author = {Dai, Zhenxue and Viswanathan, Hari and {Fessenden-Rahn}, Julianna and Middleton, Richard and Pan, Feng and Jia, Wei and Lee, Si-Yong and McPherson, Brian and Ampomah, William and Grigg, Reid},
  year = {2014},
  pages = {7685-7693},
  publisher = {{Elsevier}}
}

@article{ivanov2016,
  title = {Upscaling in Orthorhombic Media: {{Behavior}} of Elastic Parameters in Heterogeneous Fractured Earth},
  volume = {81},
  doi = {10.1190/geo2015-0392.1},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Ivanov, Yuriy and Stovas, Alexey},
  year = {2016},
  pages = {C113-C126},
  eprint = {https://doi.org/10.1190/geo2015-0392.1}
}

@article{stovas2017,
  title = {Kinematic Parameters of Pure- and Converted-Mode Waves in Elastic Orthorhombic Media},
  volume = {65},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12420},
  number = {2},
  journal = {Geophysical Prospecting},
  author = {Stovas, Alexey},
  year = {2017},
  pages = {426-452}
}

@article{kosloff1982,
  title = {Forward Modeling by a {{Fourier}} Method},
  volume = {47},
  doi = {10.1190/1.1441288},
  abstract = {A Fourier or pseudospectral forward-modeling algorithm for solving the two-dimensional acoustic wave equation is presented. The method utilizes a spatial numerical grid to calculate spatial derivatives by the fast Fourier transform. Time derivatives which appear in the wave equation are calculated by second-order differencing. The scheme requires fewer grid points than finite-difference methods to achieve the same accuracy. It is therefore believed that the Fourier method will prove more efficient than finite-difference methods, especially when dealing with three-dimensional models.The Fourier forward-modeling method was tested against two problems, a single-layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling. The numerical results agreed with both the analytic and physical model results. Furthermore, the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account.},
  number = {10},
  journal = {Geophysics},
  author = {Kosloff, Dan D. and Baysal, Edip},
  year = {1982},
  pages = {1402-1412},
  eprint = {http://geophysics.geoscienceworld.org/content/47/10/1402.full.pdf+html}
}

@article{beydoun1989,
  title = {Elastic {{Ray}}-{{Born}} L2-{{Migration}}/{{Inversion}}},
  volume = {97},
  doi = {10.1111/j.1365-246X.1989.tb00490.x},
  abstract = {The approximate ray Green's tensor in 3-D heterogeneous elastic media combined with the first-order Born approximation lead to new explicit equations for solving, modelling and inverse scattering problems. Individual wave scattering contributions (PP, PS, SP, SS) are represented for four different linear approximations (i.e. parameter linearizations). the first-order Born appoximation yields a scattered wavefield which is linearly related to medium parameter perturbations. the linearized inverse scattering problem is solved in the space-time domain and consists of minimizing a cost function within the l2 norm with a one-step conditioned gradient procedure. From uni- or multicomponent data and a reference heterogeneous background model representing adequately either the long spatial wavelengths of the medium (i.e. the smooth model), and/or its principal features (i.e. the macro-model), this operation reduces to: (1) pre-stack depth-migrating the scattered data yielding three intermediate images; and (2) deconvolving these images by an elastic Hessian correction which produces final high-resolution images representing the medium's short spatial wavelength variations convolved with the source function (e.g. P and S impedances and density maps). If the reference model and data are satisfactory, typical artefacts are due to limited aperture or insufficient coverage. Use of high-frequency and Born approximations require certain constraints. For example, the dominant wavelength must always be smaller than the characteristic length of the reference medium, but larger than the scatterer characteristic length. to increase computational efficiency, the high-frequency approximate Green's tensor is calculated by the paraxial ray method. 2-D elastic synthetic examples for surface reflection and cross-hole experiments show the ability of such a technique to delineate subsurface structure and to recover local changes in elastic properties. However, density variations are more difficult to resolve than P and S impedance or velocity changes.},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Beydoun, Wafik B. and Mendes, Manuela},
  year = {1989},
  pages = {151-160},
  eprint = {http://gji.oxfordjournals.org/content/97/1/151.full.pdf+html}
}

@article{juwon2016,
  title = {Elastic Orthorhombic Anisotropic Parameter Inversion: {{An}} Analysis of Parameterization},
  volume = {81},
  doi = {10.1190/geo2015-0656.1},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Oh, Ju-Won and Alkhalifah, Tariq},
  year = {2016},
  pages = {C279-C293},
  eprint = {http://dx.doi.org/10.1190/geo2015-0656.1}
}

@article{artman2010,
  title = {Image Domain Signal to Noise Estimate},
  author = {Artman, Brad and Witten, Benjamin},
  month = jan,
  year = {2010},
  publisher = {{Google Patents}},
  note = {US Patent App. 13/145,328}
}

@article{kamei2013,
  title = {On Acoustic Waveform Tomography of Wide-Angle {{OBS}} Data?Strategies for Pre-Conditioning and Inversion},
  volume = {194},
  doi = {10.1093/gji/ggt165},
  abstract = {We successfully apply the acoustic Laplace?Fourier waveform tomography method to delineate P-wave velocity structures of the mega-splay fault system in the central part of the seismogenic Nankai subduction zone offshore Japan, using densely sampled wide-angle ocean bottom seismograph (OBS) data originally acquired in 2004. Our success is due to new and carefully designed data preconditioning and inversion strategies to mitigate (i) the well-known non-linearity of waveform inversion, (ii) the challenges arising from crustal-scale survey designs (e.g. undersampling of the OBSs), and (iii) modelling errors due to the use of the acoustic assumption.We identify a sixfold set of key components that together lead to the success of the high-resolution waveform tomography image: (i) Availability of low-frequency components (starting at 2.25?Hz) reducing the non-linearity, and access to large offset data (up to 55?km) increasing the depth of illumination and the recovery of low wavenumber components. (ii) A highly accurate traveltime tomography result (with an rms error of approximately 60?ms) that further mitigates the non-linearity. (iii) A hierarchical inversion approach in which phase spectra are inverted first to reduce artefacts from the acoustic assumption, and amplitude information is only incorporated in the final stages. (iv) A Laplace?Fourier domain approach that facilitates a multiscale approach to mitigate non-linearity by restricting the inversion to the low frequency components and early arrivals first, and sequentially including higher frequencies and later arrivals. (v) A pre-conditioning strategy for eliminating undesirable high wavenumber components from the the gradient. (vi) A strategy for source estimation that reduce the influence of the instrumental design.In the OBS case study used for illustration purposes, Laplace?Fourier waveform tomography retrieves velocity anomalies as small as 700?m (horizontally) and 350?m (vertically) above the top of the Philippine Sea Plate. The resulting velocity structures include low-velocity zones and thrust structures which have not been previously identified clearly. The velocity models are validated by scrutiny of synthetic and observed waveforms, by evaluating the coherency of source estimates, and by comparison with 3-D pre-stack migrated (PreSDM) images. Chequerboard tests and point-scatter tests demonstrate both the reliability and the limitations of the acoustic implementation.},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Kamei, R. and Pratt, R. G. and Tsuji, T.},
  year = {2013},
  pages = {1250-1280},
  eprint = {http://gji.oxfordjournals.org/content/194/2/1250.full.pdf+html}
}

@article{tarantola1986,
  title = {A Strategy for Nonlinear Elastic Inversion of Seismic Reflection Data},
  volume = {51},
  number = {10},
  journal = {Geophysics},
  author = {Tarantola, Albert},
  year = {1986},
  pages = {1893-1903},
  publisher = {{Society of Exploration Geophysicists}}
}

@incollection{kazei2016,
  title = {Scattering Angle-Based Filtering via Extension in Velocity},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2016},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Kazei, Vladimir and Tessmer, Ekkehart and Alkhalifah, Tariq},
  year = {2016},
  pages = {1157-1162}
}

@article{bohlen2016Adams,
  title = {Three-Dimensional Viscoelastic Time-Domain Finite-Difference Seismic Modelling Using the Staggered {{Adams}}--{{Bashforth}} Time Integrator},
  volume = {204},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Bohlen, Thomas and Wittkamp, Florian},
  year = {2016},
  pages = {1781-1788},
  publisher = {{Oxford University Press}}
}

@article{dai2013integrated,
  title = {An Integrated Framework for Optimizing {{CO2}} Sequestration and Enhanced Oil Recovery},
  volume = {1},
  number = {1},
  journal = {Environmental Science \& Technology Letters},
  author = {Dai, Zhenxue and Middleton, Richard and Viswanathan, Hari and {Fessenden-Rahn}, Julianna and Bauman, Jacob and Pawar, Rajesh and Lee, Si-Yong and McPherson, Brian},
  year = {2013},
  pages = {49-54},
  publisher = {{ACS Publications}}
}

@article{anikiev2014m,
  title = {Methods of Seismic Waveform Inversion},
  volume = {11},
  number = {1},
  journal = {Seismic Technology},
  author = {Anikiev, DV and Kazei, VV and Kashtan, BM and Ponomarenko, AV and Troyan, VN and Shigapov, RA},
  year = {2014},
  pages = {1-32}
}

@techreport{walter2007,
  title = {Empirical Observations of Earthquake-Explosion Discrimination Using {{P}}/{{S}} Ratios and Implications for the Sources of Explosion {{S}}-Waves},
  institution = {{LAWRENCE LIVERMORE NATIONAL LAB CA}},
  author = {Walter, William R and Matzel, Eric and Pasyanos, Michael E and Harris, David B and Gok, Rengin and Ford, Sean R},
  year = {2007}
}

@article{ovcharenko2018,
  title = {Variance-Based Salt Body Reconstruction for Improved Full-Waveform Inversion},
  journal = {Geophysics},
  author = {Ovcharenko, Oleg and Kazei, Vladimir and Peter, Daniel and Alkhalifah, Tariq},
  year = {2018}
}

@article{bonaCoordinatefreeCharacterizationSymmetry2007,
  title = {Coordinate-Free {{Characterization}} of the {{Symmetry Classes}} of {{Elasticity Tensors}}},
  volume = {87},
  issn = {0374-3535, 1573-2681},
  doi = {10.1007/s10659-007-9099-z},
  abstract = {We formulate coordinate-free conditions for identifying all the symmetry classes of the elasticity tensor and prove that these conditions are both necessary and sufficient. Also, we construct a natural coordinate system of this tensor without the a priory knowledge of the symmetry axes.},
  language = {en},
  number = {2-3},
  journal = {Journal of Elasticity},
  author = {B\'ona, Andrej and Bucataru, Ioan and Slawinski, Michael A.},
  month = jun,
  year = {2007},
  pages = {109-132},
  file = {/home/kazeiv/Zotero/storage/JYWCRSJQ/Bóna et al_2007_Coordinate-free Characterization of the Symmetry Classes of Elasticity Tensors.pdf}
}

@article{browaeysDecompositionElasticTensor2004,
  title = {Decomposition of the Elastic Tensor and Geophysical Applications},
  volume = {159},
  issn = {0956540X, 1365246X},
  doi = {10.1111/j.1365-246X.2004.02415.x},
  abstract = {Elasticity is described in general by a fourth-order tensor with 21 independent coefficients, which corresponds to the triclinic symmetry class. However seismological observations are usually explained with a higher order of symmetry using fewer parameters. We propose an analytical method to decompose the elastic tensor into a sum of orthogonal tensors belonging to the different symmetry classes. The method relies on a vectorial description of the elastic tensor. Any symmetry class constitutes a subspace of a class of lower symmetry and an orthogonal projection on this subspace removes the lower symmetry part. Orthogonal projectors on each higher symmetry class are given explicitly. In addition, the method provides optimal higher symmetry approximations, which allow us to decrease the number of independent parameters. Consequences of the symmetry approximation of the elastic tensor on shear wave splitting (SWS) are investigated for upper-mantle minerals (olivine and enstatite), natural samples and numerically deformed olivine aggregates. The orthorhombic part of the elastic tensor as well as the presence of enstatite are important second-order effects.},
  language = {en},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Browaeys, Jules Thomas and Chevrot, S\'ebastien},
  month = nov,
  year = {2004},
  pages = {667-678},
  file = {/home/kazeiv/Zotero/storage/DUXHHPV7/Browaeys and Chevrot - 2004 - Decomposition of the elastic tensor and geophysica.pdf}
}

@article{moakherClosestElasticTensor2006,
  title = {The {{Closest Elastic Tensor}} of {{Arbitrary Symmetry}} to an {{Elasticity Tensor}} of {{Lower Symmetry}}},
  volume = {85},
  issn = {0374-3535, 1573-2681},
  doi = {10.1007/s10659-006-9082-0},
  language = {en},
  number = {3},
  journal = {Journal of Elasticity},
  author = {Moakher, Maher and Norris, Andrew N.},
  month = oct,
  year = {2006},
  pages = {215-263},
  file = {/home/kazeiv/Zotero/storage/M2NISRXR/Moakher and Norris - 2006 - The Closest Elastic Tensor of Arbitrary Symmetry t.pdf;/home/kazeiv/Zotero/storage/ZZCXSFSK/10.1007s10659-006-9082-0.pdf}
}

@article{fukaoEvidenceCorereflectedShear1984,
  title = {Evidence from Core-Reflected Shear Waves for Anisotropy in the {{Earth}}'s Mantle},
  volume = {309},
  copyright = {1984 Nature Publishing Group},
  issn = {1476-4687},
  doi = {10.1038/309695a0},
  abstract = {Seismologists have begun to recognize that the upper mantle at depth is anisotropic and that seismological data are not fully explicable if anisotropy is ignored1\textendash{}5. On entering an anisotropic zone a plane shear wave splits into two orthogonally polarized phases6; an effect observed by several researchers7, notably by Ando et al.5,8,9. The near vertical ScS wave, an S wave reflected once at the core-mantle boundary, is one of the most suitable phases to study the phenomenon of shear wave birefringence because it is isolated from other phases and because its particle motion is nearly horizontal and thus free from S to P conversion. The split ScS shear waves travel with different velocities in the anisotropic zone and consequently there is a time delay between their arrival at stations. My aim was to determine this time delay and the azimuth of polarization using the ScS records of two horizontal components from the Japanese islands for a deep shock beneath the Sea of Okhotsk. From the total of 41 stations 34 show a polarization of the maximum velocity phase in the NNW\textendash{}SSE direction with an average time advance of {$\sim$}0.8s from the minimum velocity phase. The relevant anisotropic zone seems to be deep-seated.},
  language = {en},
  number = {5970},
  journal = {Nature},
  author = {Fukao, Yoshio},
  month = jun,
  year = {1984},
  pages = {695-698},
  file = {/home/kazeiv/Zotero/storage/85AADK4K/Fukao_1984_Evidence from core-reflected shear waves for anisotropy in the Earth's mantle.pdf;/home/kazeiv/Zotero/storage/QBXA7WRT/Fukao_1984_Evidence from core-reflected shear waves for anisotropy in the Earth's mantle.pdf}
}

@article{searsElasticFullWaveform2008,
  title = {Elastic Full Waveform Inversion of Multi-Component {{OBC}} Seismic Data},
  volume = {56},
  issn = {1365-2478},
  doi = {10.1111/j.1365-2478.2008.00692.x},
  abstract = {Elastic full waveform inversion of seismic reflection data represents a data-driven form of analysis leading to quantification of sub-surface parameters in depth. In previous studies attention has been given to P-wave data recorded in the marine environment, using either acoustic or elastic inversion schemes. In this paper we exploit both P-waves and mode-converted S-waves in the marine environment in the inversion for both P- and S-wave velocities by using wide-angle, multi-component, ocean-bottom cable seismic data. An elastic waveform inversion scheme operating in the time domain was used, allowing accurate modelling of the full wavefield, including the elastic amplitude variation with offset response of reflected arrivals and mode-converted events. A series of one- and two-dimensional synthetic examples are presented, demonstrating the ability to invert for and thereby to quantify both P- and S-wave velocities for different velocity models. In particular, for more realistic low velocity models, including a typically soft seabed, an effective strategy for inversion is proposed to exploit both P- and mode-converted PS-waves. Whilst P-wave events are exploited for inversion for P-wave velocity, examples show the contribution of both P- and PS-waves to the successful recovery of S-wave velocity.},
  language = {en},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Sears, T.j. and Singh, S.c. and Barton, P.j.},
  month = nov,
  year = {2008},
  pages = {843-862},
  file = {/home/kazeiv/Zotero/storage/JJND5RR6/Sears et al_2008_Elastic full waveform inversion of multi-component OBC seismic data.pdf}
}

@article{vinnikGlobalPatternsAzimuthal1992,
  title = {Global Patterns of Azimuthal Anisotropy and Deformations in the Continental Mantle},
  volume = {111},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.1992.tb02102.x},
  abstract = {We present a summary of measurements of azimuthal anisotropy in the continental mantle based on the SKS technique and performed mostly with the active participation of the authors. The directions of polarization of the fast quasi-shear wave and the time delays between the quasi-shear waves are obtained at nearly 70 locations in all continents, except Antarctica. These data are interpreted in terms of lattice-preferred orientation of olivine which is caused by deformations in the mantle. The depth interval responsible for anisotropy is unknown but the data suggest that it may reach at least 300 km. The fast directions in SKS do not show clear correlation with the fast directions of the teleseismic P at the same seismograph stations.In the regions of present-day convergence the fast direction of anisotropy usually aligns with the plate boundary. This correlation implies that the direction of shortening is the same in the crust and the upper mantle. In the regions of rifting, the inferred direction of mantle flow usually aligns with the direction of extension in the crust.Outside the regions of recent tectonic activity we, most likely, observe a combined effect of frozen anisotropy in the subcrustal lithosphere and of recently formed anisotropy in the asthenosphere. On a global scale, in these regions there is a positive correlation between the absolute plate velocity directions and the fast directions of anisotropy. The correlation is especially strong in central and eastern parts of North America. A clear absence of any evidence of large-scale azimuthal anisotropy in the data of long-range refraction profiling for the upper 100 km of the mantle of that region implies that the effect in SKS is generated mainly at greater depths, in the asthenosphere. Orientation of olivine at these depths reflects recent and present-day flow in the mantle rather than processes of a distant geologic past.},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Vinnik, L. P. and Makeyeva, L. I. and Milev, A. and Usenko, A. Yu},
  month = dec,
  year = {1992},
  pages = {433-447},
  file = {/home/kazeiv/Zotero/storage/PEQV2DCD/Vinnik et al_1992_Global patterns of azimuthal anisotropy and deformations in the continental.pdf}
}

@article{bhuktaUpperMantleAnisotropy2017,
  title = {Upper Mantle Anisotropy Inferred from Shear Wave Splitting beneath the {{Eastern Indian Shield}} Region},
  issn = {1674-9871},
  doi = {10.1016/j.gsf.2017.12.003},
  abstract = {We estimate the shear wave splitting parameters vis-\`a-vis the thicknesses of the continental lithosphere beneath the two permanent seismic broadband stations located at Dhanbad (DHN) and Bokaro (BOKR) in the Eastern Indian Shield region. Broadband seismic data of 146 and 131 teleseismic earthquake events recorded at DHN and BOKR stations during 2007\textendash{}2014 were analyzed for the present measurements. The study is carried out using rotation-correlation and transverse component minimization methods. We retain our ``Good'', ``Fair'' and ``Null'' measurements, and estimate the splitting parameters using 13 ``Good'' results for DHN and 10 ``Good'' results for BOKR stations. The average splitting parameters ({$\phi$}, {$\delta$}t) for DHN and BOKR stations are found to be 50.76\textdegree{$\pm$}5.46\textdegree{} and 0.82~{$\pm{}~$}0.2~s and 56.30\textdegree{$\pm$}5.07\textdegree{} and 0.95~{$\pm{}~$}0.17~s, and the estimated average thicknesses of the anisotropic layers beneath these two stations are~{$\sim{}~$}94 and {$\sim$}109~km, respectively. The measured deviation of azimuth of the fast axis direction ({$\phi$}) from the absolute motion of the Indian plate ranges from {$\sim$}8\textdegree{} to 14\textdegree. The measured deviation of azimuth of the fast axis direction ({$\phi$}) from the absolute motion of the Indian plate ranges from {$\sim$}8\textdegree{} to 14\textdegree. The eastward deviation of the fast axis azimuths from absolute plate motion direction is interpreted to be caused by induced outflow from the asthenosphere. Further, the delay time found in the present analysis is close to the global average for continental shield areas, and also coherent with other studies for Indian shield regions. The five ``Null'' results and the lower delay time of {$\sim$}0.5\textendash{}0.6~s might be indicating multilayer anisotropy existing in the mantle lithosphere beneath the study area.},
  journal = {Geoscience Frontiers},
  author = {Bhukta, Kuntal and Khan, Prosanta K. and Mandal, Prantik},
  month = dec,
  year = {2017},
  keywords = {Absolute plate motion,Eastern Indian shield,Seismic anisotropy,Splitting parameters}
}

@book{babuskaSeismicAnisotropyEarth1991,
  title = {Seismic {{Anisotropy}} in the {{Earth}}},
  isbn = {978-0-7923-1321-2},
  abstract = {Structural geologists are well aware of the fact that isotropic rocks are quite exceptional in nature. Whicheverorigin, sedimentary, metamorphicormagmatic, rocks are shaped with a plane of mineral flattening, the foliation in geologists' jargon, and with a line ofmineral elongation, the lineation. Just like a good quarryman, a trained structural geologistwill detectapreferredorientationin an apparently isotropic granite. Preferred mineral orientation and thus structural anisotropy are the rule in nature. Consideringthe largevariationsinelasticcoefficientsofrock-forming minerals, itcould be predicted that, in turn, seismic anisotropy should exist and be important, provided thatdomains withasimilarstructural signatureare largeenough to affectseismic waves. This is why, in 1982 at a conference held in Frankfurt, which was oneofthe fIrst meetings devoted to the subject of seismic anisotropy, I asked Don Anderson the question of why seismologists had not considered earlier in their models the obvious constraint of anisotropy. I still remember Don's answer: "Adolphe, we knew that our isotropic models were not very good but we had no other choice. It is simply that, so far, computerswere not largeenough tointegrate the anisotropy parameter." Changingisotropic glassesfor anisotropic ones permits us to obtain betterand more realistic seismic modelsofthe Earth's interior, but, maybe more importantly, it has, for a seismologist, the farreaching consequenceofsteppinginto the fIeld ofgeodynamics.},
  language = {en},
  publisher = {{Springer Science \& Business Media}},
  author = {Babuska, V. and Cara, M.},
  month = jul,
  year = {1991},
  keywords = {Science / Earth Sciences / Geology,Science / Physics / Geophysics}
}

@article{silverShearWaveSplitting1991,
  title = {Shear Wave Splitting and Subcontinental Mantle Deformation},
  volume = {96},
  issn = {2156-2202},
  doi = {10.1029/91JB00899},
  abstract = {We have made measurements of shear wave splitting in the phases SKS and SKKS at 21 broadband stations in North America, South America, Europe, Asia, and Africa. Measurements are made using a retrieval scheme that yields the azimuth of the fast polarization direction {$\phi$} and delay time {$\delta$}t of the split shear wave plus uncertainties. Detectable anisotropy was found at most stations, suggesting that it is a general feature of the subcontinental mantle. Delay times range from 0.65 s to 1.70 s and average about 1 s. Somewhat surprisingly, the largest delay time is found in the 2.7 b.y.-old Western Superior Province of the Canadian Shield. The splitting observations are interpreted in terms of the strain-induced lattice preferred orientation of mantle minerals, especially olivine. We consider three hypotheses concerning the origin of the continental anisotropy: (1) strain associated with absolute plate motion, as in the oceanic upper mantle, (2) crustal stress, and (3) the past and present internal deformation of the subcontinental upper mantle by tectonic episodes. It is found that the last hypothesis is the most successful, namely that the most recent significant episode of internal deformation appears to be the best predictor of {$\phi$}. For stable continental regions, this is interpreted as ``fossil'' anisotropy, whereas for presently active regions, such as Alaska, the anisotropy reflects present-day tectonic activity. In the stable portion of North America there is a good correlation between delay time and lithospheric thickness; this is consistent with the anisotropy being localized in the subcontinental lithosphere and suggests that intrinsic anisotropy is approximately constant. The acceptance of this hypothesis has several implications for subcontinental mantle deformation. First, it argues for coherent deformation of the continental lithosphere (crust and mantle) during orogenies. This implies that the anisotropic portion of the lithosphere was present since the deformational episode and rules out the addition of undeformed material to this layer by subsequent ``underplating'' or conductive growth of the thermal boundary layer. One of the most important issues in the study of orogenies is the need to reconcile the formation of thickened lithosphere with the paradoxically high mantle temperatures often associated with orogenic episodes. Most efforts to date have focussed on modes of deformation whereby the cold lithospheric mantle is removed (by convective instability or delamination) and replaced by warm asthenosphere. These models, however, are incompatible with the evidence for preserved coherent lithospheric deformation; rather, the deformed mantle appears to have been heated in place. We suggest that the elevated mantle temperatures may be due to the strain heating accompanying the deformation.},
  language = {en},
  number = {B10},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Silver, Paul G. and Chan, W. Winston},
  month = sep,
  year = {1991},
  keywords = {7218 Lithosphere},
  pages = {16429-16454},
  file = {/home/kazeiv/Zotero/storage/DC3PLE5M/Silver_Chan_1991_Shear wave splitting and subcontinental mantle deformation.pdf}
}

@article{ponomarenkoSurfaceWaveInversion2017,
  title = {Surface-wave Inversion for a {{P}}-velocity Profile with a Constant Depth Gradient of the Squared Slowness},
  volume = {65},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12450},
  abstract = {Surface waves are often used to estimate a near-surface shear-velocity profile. The inverse problem is solved for the locally one-dimensional problem of a set of homogeneous horizontal elastic layers....},
  language = {en},
  number = {4},
  journal = {Geophysical Prospecting},
  author = {Ponomarenko, A. V. and Kashtan, B. M. and Troyan, V. N. and Mulder, W. A.},
  month = jul,
  year = {2017},
  keywords = {P-wave velocity profile,Squared-slowness gradient,Surface-wave inversion},
  pages = {941-955},
  file = {/home/kazeiv/Zotero/storage/3FQ354IU/Ponomarenko et al_2017_Surface-wave inversion for a P-velocity profile with a constant depth gradient.pdf;/home/kazeiv/Zotero/storage/PHLBNAVQ/Ponomarenko et al_2017_Surface‐wave inversion for a P‐velocity profile with a constant depth gradient.pdf}
}

@incollection{sniederChapterScatteringSurface2002,
  address = {London},
  title = {Chapter 1.7.3 - {{Scattering}} of {{Surface Waves}}},
  isbn = {978-0-12-613760-6},
  abstract = {This chapter describes the seismic imaging. It will discuss how the waveform inversion problem can be formulated in terms of statistical inference. Statistical methods are essential in order to be able to take into account the limited, uncertain nature of the observations. It can be seen that the classical imaging methods of seismology and ultrasonics (such as migration and diffraction tomography) arise as special cases of more general waveform inversion formulae. The methods described are applicable in many fields that make use of array-based waveform measurements, such as ultrasonics, nondestructive testing, global seismology, ocean acoustics and ground-penetrating radar. Seismic migration is applied in vast quantities of exploration seismic data around the world; it can be looked upon as a special case of a more general family of waveform inversion algorithms. The goal of migration is to produce maps of the subsurface reflection coefficient. Migration is used as a form of exploratory data analysis. On the other hand, the goal of seismic waveform inversion is to make quantitative inferences about the Earth's elastic properties. The final result consists of probabilistic statements about the range of models that fit the surface seismic data and are statistically consistent with the borehole measurements.},
  booktitle = {Scattering},
  publisher = {{Academic Press}},
  author = {Snieder, Roel},
  editor = {Pike, Roy and Sabatier, Pierre},
  year = {2002},
  pages = {562-577},
  file = {/home/kazeiv/Zotero/storage/CKGAX9D9/Snieder_2002_Chapter 1.pdf;/home/kazeiv/Zotero/storage/E35CJM2S/Snieder_2002_Chapter 1.pdf},
  doi = {10.1016/B978-012613760-6/50029-2}
}

@article{wookeyLowermostMantleAnisotropy2005,
  title = {Lowermost Mantle Anisotropy beneath the North {{Pacific}} from Differential {{S}}\textemdash{{ScS}} Splitting},
  volume = {161},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2005.02623.x},
  abstract = {Seismic anisotropy is an important tool for studying the nature, origin and dynamics of the lowermost mantle (D{${''}$}). We introduce differential S\textendash{}ScS splitting as a tool for removing the effect of near-source and near-receiver anisotropy to estimate splitting accrued in the D{${''}$} region. This is applicable to events recorded at epicentral distances between 60\textdegree{} and 85\textdegree. Near-source anisotropy has often been ignored in previous studies of lowermost mantle anisotropy. We apply differential S\textendash{}ScS splitting to records from Canadian National Seismic Network stations of western Pacific earthquakes; these sample the lowermost mantle beneath the north Pacific. The residual splitting in ScS, which we attribute to D{${''}$}, shows lag times between 1.0 and 3.9 s. Given the near horizontal ray path of ScS in D{${''}$}, we interpret the recovered fast directions as the orientation of the fast shear wave in the plane defined by the vertical and transverse directions and observe a clearly non-VTI (transverse isotropy with a vertical axis of symmetry) style of anisotropy. The largest population of results shows an approximately southeasterly dipping symmetry axis which we speculate might be explained by descending palaeoslab material being swept horizontally across the core\textendash{}mantle boundary towards an upwelling region beneath the central Pacific. Non-VTI symmetry and the many possible contributions to D{${''}$} anisotropy from lower-mantle minerals, melt and subducted materials suggest that our understanding of the lowermost mantle could be greatly improved by trying to resolve a more general style of anisotropy.},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Wookey, James and Kendall, J.-Michael and R\"umpker, Georg},
  month = jun,
  year = {2005},
  pages = {829-838},
  file = {/home/kazeiv/Zotero/storage/CYKSS9C7/Wookey et al_2005_Lowermost mantle anisotropy beneath the north Pacific from differential S—ScS.pdf}
}

@article{irving2017,
  title = {Using {{PKiKP}} Coda to Study Heterogeneity in the Top Layer of the Inner Core's Western Hemisphere},
  volume = {209},
  issn = {0956-540X},
  doi = {10.1093/gji/ggx047},
  abstract = {Significant lateral and depth variations of the inner core's properties, such as the large-scale hemispherical pattern, have been confirmed by a variety of seismological observations. However it is still unclear which dynamic processes in the core are responsible for these variations. Small-scale volumetric heterogeneity has been detected in the top layer of the inner core by PKiKP coda observations. Studies of these small-scale heterogeneities can provide critical information, such as the degree of alignment of iron crystals, the presence of possible partial melt and the grain size of iron crystals, all of which can be used to constrain the dynamic processes of the inner core. However, most previous observations sampled the inner core beneath the Pacific Ocean and Asia, often in the inner core's `eastern hemisphere'. We use seismic stations in the North America, including the Earthscope Transportable Array, to look at PKiKP and its coda waves. We find 21 events with clear signals. In agreement with previous studies, inner core scattering (ICS), resulting in clear PKiKP coda, is found at epicentral distances of 60\textdegree\textendash{}95\textdegree. However, the ICS we observe in these 21 western hemisphere events is weaker than previously reported for the eastern hemisphere. Comparing our observations with numerical simulations, we conclude that this relatively weak ICS indicates small-scale heterogeneity in at least the top layer of the inner core beneath Central America. Combining our clear observations with previous studies suggests either a hemispherical difference, or a regional variation, of small-scale heterogeneity in the inner core.},
  language = {en},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Wu, Wenbo and Irving, Jessica C. E.},
  month = may,
  year = {2017},
  pages = {672-687},
  file = {/home/kazeiv/Zotero/storage/FHZZVHPE/Wu_Irving_2017_Using PKiKP coda to study heterogeneity in the top layer of the inner core's.pdf}
}

@article{irvingRegionalSeismicVariations2015,
  title = {Regional Seismic Variations in the Inner Core under the {{North Pacific}}},
  volume = {203},
  issn = {0956-540X},
  doi = {10.1093/gji/ggv435},
  abstract = {An asymmetry between a nearly isotropic, faster `eastern' hemisphere and an anisotropic, slower `western' hemisphere in Earth's inner core has been revealed by previous seismic studies. However, it remains unclear if division of the inner core into just two hemispheres is too simplistic. Here, we carry out regional-scale tomography using a new body wave data set to study the hemisphere boundary region beneath the northern and central Pacific Ocean and North America. If anisotropy is not considered, then a hemispherical pattern seems to be present in the study region, though the hemisphere boundary appears to be irregular. However, once the presence of anisotropy is permitted we find that this region cannot be simply separated into an anisotropic western hemisphere and an isotropic eastern hemisphere; instead the strength of the anisotropy varies regionally. The global hemispherical pattern is not observed here, instead the strongest anisotropy is observed in the centre and south west of the study region. Some of the strongest anisotropy appears to be in the `eastern' inner core, while part of the inner core assumed to be in the western hemisphere shows weaker anisotropy. Thus, this part of the inner core displays complex variations in anisotropy which differ from a simple hemispherical division. We suggest that a long-lived global heterogeneity, such as uneven heat flow through the core\textendash{}mantle boundary over a period of hundreds of millions of years, may be responsible for the observed pattern of inner core anisotropy.},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Irving, J. C. E. and Deuss, A.},
  month = dec,
  year = {2015},
  pages = {2189-2199},
  file = {/home/kazeiv/Zotero/storage/I96XQ8YV/Irving_Deuss_2015_Regional seismic variations in the inner core under the North Pacific.pdf}
}

@article{soccoSurfacewaveAnalysisBuilding2010,
  title = {Surface-Wave Analysis for Building near-Surface Velocity Models \textemdash{} {{Established}} Approaches and New Perspectives},
  volume = {75},
  issn = {0016-8033},
  doi = {10.1190/1.3479491},
  abstract = {Today, surface-wave analysis is widely adopted for building near-surface S-wave velocity models. The surface-wave method is under continuous and rapid evolution, also thanks to the lively scientific debate among different disciplines, and interest in the technique has increased significantly during the last decade. A comprehensive review of the literature in the main scientific journals provides historical perspective, methodological issues, applications, and most-promising recent approaches. Higher modes in the inversion and retrieval of lateral variations are dealt with in great detail, and the current scientific debate on these topics is reported. A best-practices guideline is also outlined.},
  number = {5},
  journal = {GEOPHYSICS},
  author = {Socco, L. and Foti, S. and Boiero, D.},
  month = sep,
  year = {2010},
  pages = {75A83-75A102},
  file = {/home/kazeiv/Zotero/storage/SL2DHDYW/Socco et al_2010_Surface-wave analysis for building near-surface velocity models — Established.pdf}
}

@article{panLovewaveWaveformInversion2015,
  title = {Love-Wave Waveform Inversion in Time Domain for Shallow Shear-Wave Velocity},
  volume = {81},
  issn = {0016-8033},
  doi = {10.1190/geo2014-0225.1},
  abstract = {High-frequency surface-wave techniques are widely used to estimate S-wave velocity of near-surface materials. Surface-wave methods based on inversions of dispersion curves are only suitable to laterally homogeneous or smoothly laterally varying heterogeneous earth models due to the layered-model assumption during calculation of dispersion curves. Waveform inversion directly fits the waveform of observed data, and it can be applied to any kinds of earth models. We have used the Love-wave waveform inversion in the time domain to estimate near-surface S-wave velocity. We used the finite-difference method as the forward modeling method. The source effect was removed by the deconvolution technique, which made our method independent of the source wavelet. We defined the difference between the deconvolved observed and calculated waveform as the misfit function. We divided the model into different sizes of blocks depending on the resolution of the Love waves, and we updated the S-wave velocity of each block via a conjugate gradient algorithm. We used two synthetic models to test the effectiveness of our method. A real-world case verified the validity of our method.},
  number = {1},
  journal = {GEOPHYSICS},
  author = {Pan, Y. and Xia, J. and Xu, Y. and Gao, L. and Xu, Z.},
  month = nov,
  year = {2015},
  pages = {R1-R14},
  file = {/home/kazeiv/Zotero/storage/WM9B36QW/Pan et al_2015_Love-wave waveform inversion in time domain for shallow shear-wave velocity.pdf}
}

@article{dokterFullWaveformInversion2017,
  title = {Full Waveform Inversion of {{SH}}- and {{Love}}-wave Data in Near-surface Prospecting},
  volume = {65},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12549},
  abstract = {We develop a two-dimensional full waveform inversion approach for the simultaneous determination of S-wave velocity and density models from SH - and Love-wave data. We illustrate the advantages of the...},
  language = {en},
  number = {S1},
  journal = {Geophysical Prospecting},
  author = {Dokter, E. and K\"ohn, D. and Wilken, D. and De Nil, D. and Rabbel, W.},
  month = dec,
  year = {2017},
  pages = {216-236},
  file = {/home/kazeiv/Zotero/storage/C66TXWDM/Dokter et al_2017_Full waveform inversion of SH‐ and Love‐wave data in near‐surface prospecting.pdf}
}

@article{liuNewApproachSeparate2017,
  title = {A New Approach to Separate Seismic Time-Lapse Time Shifts in the Reservoir and Overburden},
  volume = {82},
  issn = {0016-8033, 1942-2156},
  doi = {10.1190/geo2016-0560.1},
  language = {en},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Liu, Yi and Landr\o, Martin and Arntsen, B\o{}rge and {van der Neut}, Joost and Wapenaar, Kees},
  month = nov,
  year = {2017},
  pages = {Q67-Q78},
  file = {/home/kazeiv/Zotero/storage/VMFA96VR/geo2016_0560.1.pdf}
}

@article{landroDiscriminationPressureFluid2001,
  title = {Discrimination between Pressure and Fluid Saturation Changes from Time-Lapse Seismic Data},
  volume = {66},
  number = {3},
  journal = {Geophysics},
  author = {Landr\o, Martin},
  year = {2001},
  pages = {836--844},
  file = {/home/kazeiv/Zotero/storage/3SKTCHFN/1.pdf}
}

@article{grechkaInversionNormalMoveout2000,
  title = {Inversion of Normal Moveout for Monoclinic Media1},
  volume = {48},
  issn = {1365-2478},
  doi = {10.1046/j.1365-2478.2000.00200.x},
  abstract = {Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients ({$\epsilon$}(1,2), {$\delta$}(1,2,3) and {$\gamma$}(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters {$\epsilon$}(1,2), {$\delta$}(1,2) and {$\gamma$}(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x1 and x2 (i.e. in the shear-wave polarization directions). The remaining coefficient {$\delta$}(3) is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients {$\zeta$}(1,2,3) which control the rotation of the P-, S1- and S2-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by P\'erez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S1- and S2-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS1- and PS2-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.},
  language = {en},
  number = {3},
  journal = {Geophysical Prospecting},
  author = {Grechka, Vladimir and Contreras, Pedro and Tsvankin, Ilya},
  month = may,
  year = {2000},
  pages = {577-602},
  file = {/home/kazeiv/Zotero/storage/CNGDDBTJ/Grechka et al_2000_Inversion of normal moveout for monoclinic media1.pdf}
}

@article{tommasiStructuralReactivationPlate2009,
  title = {Structural Reactivation in Plate Tectonics Controlled by Olivine Crystal Anisotropy},
  volume = {2},
  issn = {1752-0894, 1752-0908},
  doi = {10.1038/ngeo528},
  language = {en},
  number = {6},
  journal = {Nature Geoscience},
  author = {Tommasi, Andr\'ea and Knoll, Mickael and Vauchez, Alain and Signorelli, Javier W. and Thoraval, Catherine and Log\'e, Roland},
  month = jun,
  year = {2009},
  pages = {423-427},
  file = {/home/kazeiv/Zotero/storage/C62J9QJ4/Tommasi et al_2009_Structural reactivation in plate tectonics controlled by olivine crystal.pdf;/home/kazeiv/Zotero/storage/XU8TRI48/Structural-reactivation-in-plate-tectonics-controlled-by-olivine-crystal-anisotropy.pdf}
}

@article{durhamPlasticFlowOriented1977,
  title = {Plastic Flow of Oriented Single Crystals of Olivine: 1. {{Mechanical}} Data},
  volume = {82},
  issn = {2156-2202},
  shorttitle = {Plastic Flow of Oriented Single Crystals of Olivine},
  doi = {10.1029/JB082i036p05737},
  abstract = {A total of 41 selectively oriented single crystals of olivine (Fo92) were deformed under uniaxial stresses of 100\textendash{}1800 bars in the temperature range 1150\textdegree\textendash{}1600\textdegree{}C. Under uniform stress no strain inhomogeneities were observed. For all orientations both strain rate and dislocation structure stabilized after 1\textendash{}2\% strain and remained stable to the highest strains achieved (40\%). For all orientations, creep could be represented by a power law of the form 

= A{$\sigma$}3.6 where A varied with orientation by a factor of 50. Shape change and crystallographic rotation data for some orientations could only be accounted for by a substantial dislocation climb contribution to the strain rate. All specimens were decorated to show the dislocation structure. Supplement is available with entire article on microfiche. Order from American Geophysical Union, 1909 K Street, N.W., Washington, D.C. 20006. Document J77-009. Payment must accompany order.},
  language = {en},
  number = {36},
  journal = {Journal of Geophysical Research},
  author = {Durham, W. B. and Goetze, C.},
  month = dec,
  year = {1977},
  keywords = {3602 Mineralogy; Petrology; and Crystal Chemistry: Properties of minerals,5104 Physical Properties of Rocks: Elasticity; fracture; and flow,8155 Tectonophysics: Plate tectonics},
  pages = {5737-5753},
  file = {/home/kazeiv/Zotero/storage/FYY269QK/Durham_Goetze_1977_Plastic flow of oriented single crystals of olivine.pdf}
}

@article{wu2017,
  title = {An Efficient {{Helmholtz}} Solver for Acoustic Transversely Isotropic Media},
  volume = {83},
  number = {2},
  journal = {Geophysics},
  author = {Wu, Zedong and Alkhalifah, Tariq},
  year = {2017},
  pages = {1-20},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{masson2017box,
  title = {Box Tomography: Localized Imaging of Remote Targets Buried in an Unknown Medium, a Step Forward for Understanding Key Structures in the Deep {{Earth}}},
  volume = {211},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Masson, Yder and Romanowicz, Barbara},
  year = {2017},
  pages = {141-163},
  publisher = {{Oxford University Press}}
}

@article{bozdag2016,
  title = {Global Adjoint Tomography: First-Generation Model},
  volume = {207},
  number = {3},
  journal = {Geophysical Supplements to the Monthly Notices of the Royal Astronomical Society},
  author = {Bozd{\u a}g, Ebru and Peter, Daniel and Lefebvre, Matthieu and Komatitsch, Dimitri and Tromp, Jeroen and Hill, Judith and Podhorszki, Norbert and Pugmire, David},
  year = {2016},
  pages = {1739-1766},
  publisher = {{The Royal Astronomical Society}}
}

@article{yuDetectabilityTemporalChanges2016,
  title = {Detectability of Temporal Changes in Fine Structures near the Inner Core Boundary beneath the Eastern Hemisphere},
  volume = {43},
  issn = {1944-8007},
  doi = {10.1002/2016GL069664},
  abstract = {The inner core boundary (ICB), where melting and solidification of the core occur, plays a crucial role in the dynamics of the Earth's interior. To probe temporal changes near the ICB beneath the eastern hemisphere, I analyze differential times of PKiKP (dt(PKiKP)), double differential times of PKiKP-PKPdf, and PKiKP coda waves from repeating earthquakes in the southwest Pacific subduction zones. dt(PKiKP) values are mostly within {$\pm$}30\,ms of one another, without systematic temporal dependence. Some observations of PKiKP coda waves have absolute time shifts of {$>$}50\,ms relative to their main phases. The combination of temporal changes in PKiKP coda arrivals and negligible changes in PKiKP arrivals favors a smooth ICB with fine-scale structures in the upper inner core. dt(PKiKP) values are interpreted in the context of melting- or growth-induced ICB topography, based on dynamic models. Uncertainties in dt(PKiKP) prevent verification of ICB melting or growth on decadal time scales.},
  language = {en},
  number = {13},
  journal = {Geophysical Research Letters},
  author = {Yu, W.},
  month = jul,
  year = {2016},
  keywords = {1507 Core processes,7203 Body waves,7207 Core,8124 Earth's interior: composition and state,coda wave interferometry,inner core boundary,PKP waves,repeating earthquakes},
  pages = {2016GL069664},
  file = {/home/kazeiv/Zotero/storage/5G3RALXI/Yu - 2016 - Detectability of temporal changes in fine structur.pdf;/home/kazeiv/Zotero/storage/Q3HND52J/Yu_2016_Detectability of temporal changes in fine structures near the inner core.pdf}
}

@article{shaw2004,
  title = {Born Integral, Stationary Phase and Linearized Reflection Coefficients in Weak Anisotropic Media},
  volume = {158},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Shaw, Ranjit K and Sen, Mrinal K},
  year = {2004},
  pages = {225-238},
  publisher = {{Oxford University Press}}
}

@inproceedings{podgornova,
  title = {Analysis of Resolution Limits of {{VTI}} Anisotropy with Full Waveform Inversion},
  booktitle = {2015 {{SEG Annual Meeting}}},
  author = {Podgornova, Olga and Leaney, Scott and Liang, Lin and others},
  year = {2015},
  organization = {{Society of Exploration Geophysicists}}
}

@article{kazei2013gp,
  title = {On the Role of Reflections, Refractions and Diving Waves in Full-Waveform Inversion},
  volume = {61},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Kazei, VV and Troyan, VN and Kashtan, BM and Mulder, WA},
  year = {2013},
  pages = {1252-1263},
  publisher = {{Wiley Online Library}}
}

@article{tsvankin1997,
  title = {Anisotropic Parameters and {{P}}-Wave Velocity for Orthorhombic Media},
  volume = {62},
  number = {4},
  journal = {Geophysics},
  author = {Tsvankin, Ilya},
  year = {1997},
  pages = {1292-1309},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{wu1985,
  title = {Scattering Characteristics of Elastic Waves by an Elastic Heterogeneity},
  volume = {50},
  number = {4},
  journal = {Geophysics},
  author = {Wu, R-S and Aki, Keiiti},
  year = {1985},
  pages = {582-595},
  publisher = {{Society of Exploration Geophysicists}}
}

@incollection{duveneck2008,
  title = {Acoustic {{VTI}} Wave Equations and Their Application for Anisotropic Reverse-Time Migration},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2008},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Duveneck, Eric and Milcik, Paul and Bakker, Peter M and Perkins, Colin},
  year = {2008},
  pages = {2186-2190}
}

@article{operto2013,
  title = {A Guided Tour of Multiparameter Full-Waveform Inversion with Multicomponent Data: {{From}} Theory to Practice},
  volume = {32},
  number = {9},
  journal = {The Leading Edge},
  author = {Operto, St\'ephane and Gholami, Yaser and Prieux, V and Ribodetti, Alessandra and Brossier, R and Metivier, L and Virieux, Jean},
  year = {2013},
  pages = {1040-1054},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{gholami20132,
  title = {Which Parameterization Is Suitable for Acoustic Vertical Transverse Isotropic Full Waveform Inversion? {{Part}} 2: {{Synthetic}} and Real Data Case Studies from {{Valhall}}},
  volume = {78},
  doi = {10.1190/geo2012-0203.1},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Gholami, Yaser and Brossier, Romain and Operto, St\'ephane and Prieux, Vincent and Ribodetti, Alessandra and Virieux, Jean},
  year = {2013},
  pages = {R107-R124},
  eprint = {http://dx.doi.org/10.1190/geo2012-0203.1}
}

@article{igel1995,
  title = {Anisotropic Wave Propagation through Finite-Difference Grids},
  volume = {60},
  number = {4},
  journal = {Geophysics},
  author = {Igel, Heiner and Mora, Peter and Riollet, Bruno},
  year = {1995},
  pages = {1203-1216},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{hudson1981,
  title = {The Use of the {{Born}} Approximation in Seismic Scattering Problems},
  volume = {66},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Hudson, JA and Heritage, JR},
  year = {1981},
  pages = {221-240},
  publisher = {{Oxford University Press}}
}

@article{beylkin1990,
  title = {Linearized Inverse Scattering Problems in Acoustics and Elasticity},
  volume = {12},
  number = {1},
  journal = {Wave motion},
  author = {Beylkin, G and Burridge, R},
  year = {1990},
  pages = {15-52},
  publisher = {{Elsevier}}
}

@article{bohlen2002,
  title = {Parallel 3-{{D}} Viscoelastic Finite Difference Seismic Modelling},
  volume = {28},
  number = {8},
  journal = {Computers \& Geosciences},
  author = {Bohlen, Thomas},
  year = {2002},
  pages = {887-899},
  publisher = {{Elsevier}}
}

@article{saenger2004,
  title = {Finite-Difference Modeling of Viscoelastic and Anisotropic Wave Propagation Using the Rotated Staggered Grid},
  volume = {69},
  number = {2},
  journal = {Geophysics},
  author = {Saenger, Erik H and Bohlen, Thomas},
  year = {2004},
  pages = {583-591},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{virieux1986,
  title = {P-{{SV}} Wave Propagation in Heterogeneous Media: {{Velocity}}-Stress Finite-Difference Method},
  volume = {51},
  number = {4},
  journal = {Geophysics},
  author = {Virieux, Jean},
  year = {1986},
  pages = {889-901},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{kohn2015,
  title = {Waveform Inversion in Triclinic Anisotropic Media\textemdash{}a Resolution Study},
  volume = {201},
  number = {3},
  journal = {Geophysical Journal International},
  author = {K\"ohn, D and Hellwig, O and De Nil, D and Rabbel, W},
  year = {2015},
  pages = {1642-1656},
  publisher = {{Oxford University Press}}
}

@article{kamath2016,
  title = {Elastic Full-Waveform Inversion for {{VTI}} Media: {{Methodology}} and Sensitivity Analysis},
  volume = {81},
  doi = {10.1190/geo2014-0586.1},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Kamath, Nishant and Tsvankin, Ilya},
  year = {2016},
  pages = {C53-C68},
  eprint = {http://dx.doi.org/10.1190/geo2014-0586.1}
}

@incollection{kazei2015seg,
  title = {{{FWI}} Spectral Sensitivity Analysis in the Presence of a Free Surface},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2015},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Kazei, VV and Kashtan, BM and Troyan, VN and Mulder, WA},
  year = {2015},
  pages = {1415-1419}
}

@article{calvet2006,
  title = {P-Wave Propagation in Transversely Isotropic Media: {{I}}. {{Finite}}-Frequency Theory},
  volume = {156},
  issn = {0031-9201},
  doi = {http://dx.doi.org/10.1016/j.pepi.2006.01.004},
  number = {1\textendash{}2},
  journal = {Physics of the Earth and Planetary Interiors},
  author = {Calvet, Marie and Chevrot, S\'ebastien and Souriau, Annie},
  year = {2006},
  keywords = {Fréchet derivatives},
  pages = {12-20}
}

@book{cerveny2005,
  title = {Seismic Ray Theory},
  publisher = {{Cambridge university press}},
  author = {Cerveny, Vlastislav},
  year = {2005}
}

@article{kiya2004,
  title = {Anisotropic Migration Weight for Amplitude-Preserving Migration and Sensitivity Analysis},
  volume = {157},
  doi = {10.1111/j.1365-246X.2004.02242.x},
  abstract = {An amplitude-preserving anisotropic migration formula is derived in this paper. The migration is viewed as a weighted diffraction stack and the migration weights are estimated with the stationary phase theorem. To obtain a formula easy to implement, the weights are written in terms of quantities computable along the rays. A sensitivity analysis is then carried out to show that, in the vertical transverse isotropic case, the amplitude-preserving migration is mainly governed by two parameters: the anisotropic NMO velocity and the parameter {$\eta$}. These parameters can be estimated from the data with a velocity (background) analysis. Therefore, it is possible to use this amplitude-preserving anisotropic migration to recover the correct amplitudes versus offset or azimuth in the migrated image.},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Kiyashchenko, D. and Kashtan, B. and Plessix, R.-E.},
  year = {2004},
  pages = {753-763},
  eprint = {http://gji.oxfordjournals.org/content/157/2/753.full.pdf+html}
}

@article{podgornova2016,
  title = {Anisotropic Elastic Full-waveform Inversion of Walkaway Vertical Seismic Profiling Data from the {{Arabian Gulf}}},
  volume = {64},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12227},
  abstract = {Borehole seismic addresses the need for high-resolution images and elastic parameters of the subsurface. Full-waveform inversion of vertical seismic profile data is a promising technology with the potential to recover quantitative information about elastic properties of the medium. Full-waveform inversion has the capability to process the entire wavefield and to address the wave propagation effects contained in the borehole data\textemdash{}multi-component measurements; anisotropic effects; compressional and shear waves; and transmitted, converted, and reflected waves and multiples. Full-waveform inversion, therefore, has the potential to provide a more accurate result compared with conventional processing methods. We present a feasibility study with results of the application of high-frequency (up to 60 Hz) anisotropic elastic full-waveform inversion to a walkaway vertical seismic profile data from the Arabian Gulf. Full-waveform inversion has reproduced the majority of the wave events and recovered a geologically plausible layered model with physically meaningful values of the medium.},
  number = {1},
  journal = {Geophysical Prospecting},
  author = {Owusu, John C and Podgornova, Olga and Charara, Marwan and Leaney, Scott and Campbell, Allan and Ali, Shujaat and Borodin, Igor and Nutt, Les and Menkiti, Henry},
  month = jan,
  year = {2016},
  pages = {38-53},
  publisher = {{Wiley Online Library}}
}

@article{gholami20131,
  title = {Which Parameterization Is Suitable for Acoustic Vertical Transverse Isotropic Full Waveform Inversion? {{Part}} 1: {{Sensitivity}} and Trade-off Analysis},
  volume = {78},
  doi = {10.1190/geo2012-0204.1},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Gholami, Yaser and Brossier, Romain and Operto, St\'ephane and Ribodetti, Alessandra and Virieux, Jean},
  year = {2013},
  pages = {R81-R105},
  eprint = {http://dx.doi.org/10.1190/geo2012-0204.1}
}

@inproceedings{tore2015,
  title = {The Influence of Anisotropy on Elastic Full-Waveform Inversion},
  booktitle = {2015 {{SEG Annual Meeting}}},
  author = {Bergslid, Tore S and Birger Raknes, Espen and Arntsen, B\o{}rge and others},
  year = {2015},
  organization = {{Society of Exploration Geophysicists}}
}

@incollection{snieder2002,
  address = {London},
  title = {Chapter 1.7.1 - {{General Theory}} of {{Elastic Wave Scattering}}},
  isbn = {978-0-12-613760-6},
  abstract = {Publisher Summary This chapter discusses the basic elements of elastodynamic wave scattering theory. It is based on two foundations continuum mechanics of elastic media and the general principles of scattering theory. There is a wide body of literature on elastodynamic wave scattering. A comprehensive overview of scattering of acoustic, electromagnetic, and elastic waves are presented in a unified way. The propagation of elastic waves forms the foundation of seismology. An outline is given on the principles of elasticity that are relevant for elastic wave scattering. In elasticity theory, the Green's function gives the displacement generated by a point force in a certain direction. Since both the point force and the displacement are vectors with three components, the Green's function is a 3 x 3 tensor. To describe scattering, it is necessary to define a reference medium in which an unperturbed wave propagates and a perturbation of the medium that acts as a secondary source generates scattered waves. For this reason, the elasticity tensor c is divided into a reference tensor c(0) and a perturbation c(1).},
  booktitle = {Scattering},
  publisher = {{Academic Press}},
  author = {Snieder, Roel},
  editor = {Pike, Roy and Sabatier, Pierre},
  year = {2002},
  pages = {528-542},
  doi = {http://dx.doi.org/10.1016/B978-012613760-6/50027-9}
}

@article{warner2013,
  title = {Anisotropic {{3D}} Full-Waveform Inversion},
  volume = {78},
  issn = {0016-8033},
  doi = {10.1190/geo2012-0338.1},
  abstract = {We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7~km, with reduced coverage to a maximum offset of about 11~km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000~m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5~Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model building including anisotropic reflection tomography, and contained epsilon values as high as 20\%. The final FWI velocity model shows a network of shallow high-velocity channels that match similar features in the reflection data. Deeper in the section, the FWI velocity model reveals a sharper and more-intense low-velocity region associated with the gas cloud in which low-velocity fingers match the location of gas-filled faults visible in the reflection data. The resulting velocity model provides a better match to well logs, and better flattens common-image gathers, than does the starting model. Reverse-time migration, using the FWI velocity model, provides significant uplift to the migrated image, simplifying the planform of the reservoir section at depth. The workflows, inversion strategy, and algorithms that we have used have broad application to invert a wide-range of analogous data sets.},
  number = {2},
  journal = {Geophysics},
  author = {Warner, Michael and Ratcliffe, Andrew and Nangoo, Tenice and Morgan, Joanna and Umpleby, Adrian and Shah, Nikhil and Vinje, Vetle and Stekl, Ivan and Guasch, Llu\'is and Win, Caroline and Conroy, Graham and Bertrand, Alexandre},
  year = {2013},
  pages = {R59-R80},
  eprint = {http://geophysics.geoscienceworld.org/content/78/2/R59.full.pdf},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{alkhalifah2014,
  title = {A Recipe for Practical Full-Waveform Inversion in Anisotropic Media: {{An}} Analytical Parameter Resolution Study},
  volume = {79},
  doi = {10.1190/geo2013-0366.1},
  number = {3},
  journal = {Geophysics},
  author = {Alkhalifah, Tariq and Plessix, Rene-Edouard},
  year = {2014},
  pages = {R91-R101},
  eprint = {http://dx.doi.org/10.1190/geo2013-0366.1}
}

@book{menke2012,
  title = {Geophysical Data Analysis: {{Discrete}} Inverse Theory},
  volume = {45},
  publisher = {{Academic press}},
  author = {Menke, William},
  year = {2012}
}

@article{grechka1999,
  title = {3-{{D}} Moveout Velocity Analysis and Parameter Estimation for Orthorhombic Media},
  volume = {64},
  number = {3},
  journal = {Geophysics},
  author = {Grechka, Vladimir and Tsvankin, Ilya},
  year = {1999},
  pages = {820-837},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{plessix2016,
  title = {Analysis of Different Parameterisations of Waveform Inversion of Compressional Body Waves in an Elastic Transverse Isotropic {{Earth}} with a Vertical Axis of Symmetry},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12452},
  journal = {Geophysical Prospecting},
  author = {He, Weiguang and Plessix, Ren\'e-\'Edouard},
  year = {2016},
  keywords = {Full-waveform inversion,Anisotropy,Radiation pattern},
  pages = {n/a-n/a}
}

@article{masmoudi2016,
  title = {A New Parameterization for Waveform Inversion in Acoustic Orthorhombic Media},
  volume = {81},
  number = {4},
  journal = {Geophysics},
  author = {Masmoudi, Nabil and Alkhalifah, Tariq},
  year = {2016},
  pages = {R157-R171},
  publisher = {{Society of Exploration Geophysicists}}
}

@inproceedings{kazei2017,
  title = {On the {{Resolution}} of {{Inversion}} for {{Orthorhombic Anisotropy}}},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Kazei, VV and Alkhalifah, T},
  year = {2017}
}

@article{liu2006,
  title = {Finite-Frequency Kernels Based on Adjoint Methods},
  volume = {96},
  number = {6},
  journal = {Bulletin of the Seismological Society of America},
  author = {Liu, Qinya and Tromp, Jeroen},
  year = {2006},
  pages = {2383-2397},
  publisher = {{Seismological Society of America}}
}

@article{long2010mantle,
  title = {Mantle Dynamics and Seismic Anisotropy},
  volume = {297},
  number = {3},
  journal = {Earth and Planetary Science Letters},
  author = {Long, Maureen D and Becker, Thorsten W},
  year = {2010},
  pages = {341-354},
  publisher = {{Elsevier}}
}

@article{tromp1993support,
  title = {Support for Anisotropy of the {{Earth}}'s Inner Core from Free Oscillations},
  volume = {366},
  number = {6456},
  journal = {Nature},
  author = {Tromp, Jeroen},
  year = {1993},
  pages = {678-681}
}

@article{gao2006upper,
  title = {Upper Mantle Seismic Structure beneath Eastern {{Mexico}} Determined from {{P}} and {{S}} Waveform Inversion and Its Implications},
  volume = {111},
  number = {B8},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Gao, Wei and Matzel, Eric and Grand, Stephen P},
  year = {2006},
  publisher = {{Wiley Online Library}}
}

@article{zhu2017,
  title = {Radial Anisotropy of the {{North American}} Upper Mantle Based on Adjoint Tomography with {{USArray}}},
  volume = {211},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Zhu, Hejun and Komatitsch, Dimitri and Tromp, Jeroen},
  year = {2017},
  pages = {349-377},
  publisher = {{Oxford University Press}}
}

@article{simons2009potential,
  title = {On the Potential of Recording Earthquakes for Global Seismic Tomography by Low-Cost Autonomous Instruments in the Oceans},
  volume = {114},
  number = {B5},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Simons, Frederik J and Nolet, Guust and Georgief, Paul and Babcock, Jeff M and Regier, Lloyd A and Davis, Russ E},
  year = {2009},
  publisher = {{Wiley Online Library}}
}

@article{sukhovich2015seismic,
  title = {Seismic Monitoring in the Oceans by Autonomous Floats},
  volume = {6},
  journal = {Nature communications},
  author = {Sukhovich, Alexey and Bonnieux, S\'ebastien and Hello, Yann and Irisson, Jean-Olivier and Simons, Frederik J and Nolet, Guust},
  year = {2015},
  publisher = {{Nature Research}}
}

@article{alkhalifah2000,
  title = {An Acoustic Wave Equation for Anisotropic Media},
  volume = {65},
  number = {4},
  journal = {Geophysics},
  author = {Alkhalifah, Tariq},
  year = {2000},
  pages = {1239-1250},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{thomsen1986,
  title = {Weak Elastic Anisotropy},
  volume = {51},
  doi = {10.1190/1.1442051},
  number = {10},
  journal = {GEOPHYSICS},
  author = {Thomsen, Leon},
  year = {1986},
  pages = {1954-1966},
  eprint = {http://dx.doi.org/10.1190/1.1442051}
}

@inproceedings{anikiev2014,
  title = {Multiparameter {{Elastic Imaging Improved}} by {{Preconditioning}} with an {{Incomplete Inverse Hessian Approximation}}},
  booktitle = {76th {{EAGE Conference}} and {{Exhibition}} 2014},
  author = {Anikiev, DV and Kashtan, BM and Mulder, WA},
  year = {2014}
}

@article{eaton1994,
  title = {Migration/Inversion for Transversely Isotropic Elastic Media},
  volume = {119},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.1994.tb00148.x},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Eaton, David W. S. and Stewart, Robert R.},
  year = {1994},
  keywords = {anisotropy,Born approximation,inverse scattering,inversion},
  pages = {667-683},
  publisher = {{Blackwell Publishing Ltd}}
}

@article{ruger1997,
  title = {P-Wave Reflection Coefficients for Transversely Isotropic Models with Vertical and Horizontal Axis of Symmetry},
  volume = {62},
  number = {3},
  journal = {Geophysics},
  author = {R\"uger, Andreas},
  year = {1997},
  pages = {713-722},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{creager1999large,
  title = {Large-Scale Variations in Inner Core Anisotropy},
  volume = {104},
  number = {B10},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Creager, Kenneth C},
  year = {1999},
  pages = {23127-23139},
  publisher = {{Wiley Online Library}}
}

@misc{CarbonateReservoirsSchlumberger,
  title = {Carbonate {{Reservoirs}} | {{Schlumberger}}},
  howpublished = {http://www.slb.com/services/technical\_challenges/carbonates.aspx}
}

@article{dellingerComputingOptimalTransversely2005,
  title = {Computing the Optimal Transversely Isotropic Approximation of a General Elastic Tensor},
  volume = {70},
  issn = {0016-8033},
  doi = {10.1190/1.2073890},
  abstract = {Mathematically, 21 stiffnesses arranged in a 6 \texttimes{} 6 symmetric matrix completely describe the elastic properties of any homogeneous anisotropic medium, regardless of symmetry system and orientation. However, it can be difficult in practice to characterize an anisotropic medium's properties merely from casual inspection of its (often experimentally measured) stiffness matrix. For characterization purposes, it is better to decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic (TI) medium (whose properties can be readily understood) plus a generally anisotropic perturbation (representing the medium's deviation from perfect symmetry), followed by a rotation (giving the relationship between the medium's natural coordinate system and the measurement coordinate system). To accomplish this decomposition, we must find the rotated symmetric medium that best approximates a given stiffness matrix. An analytical formula exists for calculating the distance between the elastic properties of two anisotropic media. Starting from this formula, I show how to analytically calculate the TI medium with a zz{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>$}z{$<$}/mi{$><$}/mrow{$><$}/math{$>$} symmetry axis that is nearest to a given set of 21 stiffness constants. There is no known analytical result if the symmetry axis is not fixed beforehand. I therefore present a simple search algorithm that scans all possible orientations of the nearest TI medium's symmetry axis. The grid is iteratively refined to optimize the solution. The algorithm is simple and robust and works well in practice, but it is not guaranteed to always find the optimal global answer if there are secondary minima that provide almost as good a fit as the optimal one.},
  number = {5},
  journal = {GEOPHYSICS},
  author = {Dellinger, J.},
  month = sep,
  year = {2005},
  pages = {I1-I10},
  file = {/home/kazeiv/Zotero/storage/GI2PND66/Dellinger - 2005 - Computing the optimal transversely isotropic appro.pdf}
}

@article{dupuyQuantitativeSeismicCharacterization2017,
  title = {Quantitative Seismic Characterization of {{CO2}} at the {{Sleipner}} Storage Site, {{North Sea}}},
  volume = {5},
  issn = {2324-8858},
  doi = {10.1190/INT-2017-0013.1},
  abstract = {Reliable quantification of carbon dioxide (CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$}) properties and saturation is crucial in the monitoring of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} underground storage projects. We have focused on quantitative seismic characterization of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} at the Sleipner storage pilot site. We evaluate a methodology combining high-resolution seismic waveform tomography, with uncertainty quantification and rock physics inversion. We use full-waveform inversion (FWI) to provide high-resolution estimates of P-wave velocity VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and perform an evaluation of the reliability of the derived model based on posterior covariance matrix analysis. To get realistic estimates of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation, we implement advanced rock physics models taking into account effective fluid phase theory and patchy saturation. We determine through sensitivity tests that the estimation of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation is possible even when using only the P-wave velocity as input. After a characterization of rock frame properties based on log data prior to the CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} injection at Sleipner, we apply our two-step methodology. The FWI result provides clear indications of the injected CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} plume being observed as low-velocity zones corresponding to thin CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} filled layers. Several tests, varying the rock physics model and CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} properties, are then performed to estimate CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation. The results suggest saturations reaching 30\%\textendash{}35\% in the thin sand layers and up to 75\% when patchy mixing is considered. We have carried out a joint estimation of saturation with distribution type and, even if the inversion is not well-constrained due to limited input data, we conclude that the CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} has an intermediate pattern between uniform and patchy mixing, which leads to saturation levels of approximately 25\%{$\pm$}15\%25\%{$\pm$}15\%{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mn{$>$}25{$<$}/mn{$><$}mo{$>\%<$}/mo{$><$}mo{$>\pm{}<$}/mo{$><$}mn{$>$}15{$<$}/mn{$><$}mo form="postfix"{$>\%<$}/mo{$><$}/mrow{$><$}/math{$>$}. It is worth noting that the 2D section used in this work is located 533~m east of the injection point. We also conclude that the joint estimation of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} properties with saturation is not crucial and consequently that knowing the pressure and temperature state of the reservoir does not prevent reliable estimation of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation.},
  number = {4},
  journal = {Interpretation},
  author = {Dupuy, B. and Romdhane, A. and Eliasson, P. and Querendez, E. and Yan, H. and Torres, V. and Ghaderi, A.},
  month = aug,
  year = {2017},
  pages = {SS23-SS42},
  file = {/home/kazeiv/Zotero/storage/8JDWMNRM/Dupuy et al. - 2017 - Quantitative seismic characterization of CO2 at th.pdf}
}

@misc{QuantitativeSeismicCharacterization,
  title = {Quantitative Seismic Characterization of {{CO}} 2 at the {{Sleipner}} Storage Site, {{North Sea}}},
  abstract = {ResearchGate is a network dedicated to science and research. Connect, collaborate and discover scientific publications, jobs and conferences. All for free.},
  language = {en},
  journal = {ResearchGate},
  howpublished = {https://www.researchgate.net/publication/318862999\_Quantitative\_seismic\_characterization\_of\_CO\_2\_at\_the\_Sleipner\_storage\_site\_North\_Sea}
}

@article{kazei2018,
  title = {Waveform Inversion for Orthorhombic Anisotropy with {{P}}-Waves: Feasibility \&amp; Resolution},
  doi = {10.1093/gji/ggy034},
  journal = {Geophysical Journal International},
  author = {Kazei, Vladimir and Alkhalifah, Tariq},
  year = {2018},
  pages = {ggy034}
}

@article{poupinetObservationHighFrequency2004,
  title = {On the Observation of High Frequency {{PKiKP}} and Its Coda in {{Australia}}},
  volume = {146},
  issn = {0031-9201},
  doi = {10.1016/j.pepi.2004.05.003},
  abstract = {The seismic phase PKiKP, reflected from the inner core, and its coda give information on the short scale heterogeneities at and below the inner core boundary (ICB) of the Earth. We have collected PKiKP recorded at short distances ({$<$}45\textdegree{}) at broadband stations in Australia and at the Warramunga seismic array (WRA). Despite potential complications from a dual-passage through D{${''}$}, PKiKP is frequently observed on single traces in the frequency band 1\textendash{}5Hz. PKiKP usually has a sharp onset, but sometimes its waveforms have multiple pulses separated by times of the order of 1s. At WRA, the coda of PKiKP initially decays very rapidly after the main pulse. Thereafter, its amplitude is nearly constant and more than three times smaller than PKiKP with duration longer than 200s. Our observations differ from those of [Nature 404 (2000) 273\textendash{}275], at rather greater distances, who found that the coda is larger than PKiKP and increases slowly. We suggest that the PKiKP coda is generated near the inner core boundary by complex reverberation effects, rather than scattering through the volume of the inner core.},
  number = {3},
  journal = {Physics of the Earth and Planetary Interiors},
  author = {Poupinet, G and Kennett, B. L. N},
  month = sep,
  year = {2004},
  keywords = {Heterogeneities,Inner core,PKiKP,Seismic phase},
  pages = {497-511},
  file = {/home/kazeiv/Zotero/storage/CFGHXQYA/Poupinet_Kennett_2004_On the observation of high frequency PKiKP and its coda in Australia.pdf;/home/kazeiv/Zotero/storage/S8T8XSJX/S0031920104002225.html}
}

@article{tanakaComplexInnerCore2015,
  title = {Complex Inner Core Boundary from Frequency Characteristics of the Reflection Coefficients of {{PKiKP}} Waves Observed by {{Hi}}-Net},
  volume = {2},
  issn = {2197-4284},
  doi = {10.1186/s40645-015-0064-3},
  abstract = {Frequency-dependent reflection coefficients of P waves at the inner core boundary (ICB) are estimated from the spectral ratios of PKiKP and PcP waves observed by the high-sensitivity seismograph network (Hi-net) in Japan. The corresponding PKiKP reflection locations at the ICB are distributed beneath the western Pacific. At frequencies where noise levels are sufficiently low, spectra of reflection coefficients show four distinct sets of characteristics: a flat spectrum, a spectrum with a significant spectral hole at approximately 1 or 3~Hz, a spectrum with a strong peak at approximately 2 or 3~Hz, and a spectrum containing both a sharp peak and a significant hole. The variety in observed spectra suggests complex lateral variations in ICB properties. To explain the measured differences in frequency characteristics of ICB reflection coefficients, we conduct 2D finite difference simulations of seismic wavefields near the ICB. The models tested in our simulations include a liquid layer and a solid layer above the ICB, as well as sinusoidal and spike-shaped ICB topography with varying heights and scale lengths. We find that the existence of a layer above the ICB can be excluded as a possible explanation for the observed spectra. Furthermore, we find that an ICB topographic model with wavelengths and heights of several kilometers is too extreme to explain our measurements. However, restricting the ICB topography to wavelengths and heights of 1.0\textendash{}1.5~km can explain the observed frequency-related phenomena. The existence of laterally varying topography may be a sign of lateral variations in inner core solidification.},
  journal = {Progress in Earth and Planetary Science},
  author = {Tanaka, Satoru and Tkal{\v c}i\'c, Hrvoje},
  month = nov,
  year = {2015},
  keywords = {PKiKP,Finite difference modeling,Inner core boundary,Topography},
  pages = {34},
  file = {/home/kazeiv/Zotero/storage/ZMLVCBP8/Tanaka_Tkalčić_2015_Complex inner core boundary from frequency characteristics of the reflection.pdf;/home/kazeiv/Zotero/storage/DZTU6DAW/s40645-015-0064-3.html}
}

@article{pengInnercoreFinescaleStructure2008,
  title = {Inner-Core Fine-Scale Structure from Scattered Waves Recorded by {{LASA}}},
  volume = {113},
  issn = {2156-2202},
  doi = {10.1029/2007JB005412},
  abstract = {Recent observations of inner-core scattering (ICS) waves provide evidence that the outermost 300 km of the inner-core has strong heterogeneities with a length scale of a few kilometers. These waves follow a path similar to that of the inner-core\textendash{}reflected waves PKiKP and were originally observed in data from 16 events in the distance range 58\textdegree{} to 73\textdegree{} recorded by the Large Aperture Seismic Array (LASA). Here we present additional observations of the ICS waves from a total of 78 events recorded by LASA at distances from 18\textdegree{} to 98\textdegree. We use a modified version of the Generic Array Processing software package to identify ICS waves on the basis of travel time, back azimuth, ray parameter, amplitude, and coherence. There are 44 events that produce clear ICS waves. We then perform forward modeling of the observed ICS waves using a Monte Carlo seismic phonon method that allows for multiple scattering along the raypath. Most of the ICS waves appear without a visible PKiKP phase, initially grow in time, and have a spindle-shaped envelope. The duration, risetime, and decay rates of the observed ICS waves can be best explained by small-scale volumetric heterogeneities in the outermost few hundred kilometers of the inner core. The average Qc value for the 44 events is {$\sim$}600. Most clear ICS waves are found for raypaths sampling the Pacific Ocean and Asia, and relatively few observations are from the Atlantic Ocean, roughly consistent with the recently observed hemispheric difference in the inner-core structure.},
  language = {en},
  number = {B9},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Peng, Zhigang and Koper, Keith D. and Vidale, John E. and Leyton, Felipe and Shearer, Peter},
  month = sep,
  year = {2008},
  keywords = {7207 Core,8124 Earth's interior: composition and state,PKiKP,8115 Core processes,coda waves,inner core},
  pages = {B09312},
  file = {/home/kazeiv/Zotero/storage/8ULZB6EY/Peng et al_2008_Inner-core fine-scale structure from scattered waves recorded by LASA.pdf;/home/kazeiv/Zotero/storage/4ZY78K7C/abstract.html}
}

@article{bolt1970,
  title = {{{PdP}} and {{PKiKP Waves}} and {{Diffracted PcP Waves}}},
  volume = {20},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.1970.tb06080.x},
  abstract = {Travel times, listed in the I.S.S., of longitudinal waves at distances of 100\textdegree{} {$<$} {$\Delta$} {$<$} 115\textdegree{} from 16 earthquakes with depths near 100km give rather precise information on properties of the Earth (a) in the upper third of the mantle, (b) at the inner core boundary, and (c) at the bottom of the mantle. The sources are relocated using the 1968 tables of Herrin et al. Precursors to PP, called PdP, are widely reported up to about 85s before PP; few are reported at earlier times. These independent observations provide further evidence that, above a depth of at least 400 km, the upper mantle contains structural discontinuities (perhaps due to phase changes) on a global scale. PKiKP waves (reflections from the inner core) are traceable in this data sample back to 106\textdegree. The result is consistent with a sharp inner core boundary at 1220km radius. Observed PKP travel times near 113\textdegree{} are closely consistent with PKIKP times derived by Bolt for use with the 1968 P tables of Herrin et al.; the observed times for {$\Delta$} {$<$} 113\textdegree{} are about 0.5 s later than predicted. Travel times (for 100 km focal depth and 102\textdegree{} {$<$} {$\Delta$} {$<$} 110\textdegree{}) of the PcP wave which is diffracted into the shadow of the core fit the curve t= (14m 02.8{$\pm$};0.14s)+(4.60{$\pm$}0.05 s/deg)({$\Delta$}\textendash{}106\textdegree.45). This result leads to a radius for the Earth's core of 3479{$\pm$}2km; there is an indication that the P velocity may decrease by a few per cent at the base of the mantle.},
  language = {en},
  number = {4},
  journal = {Geophysical Journal of the Royal Astronomical Society},
  author = {Bolt, Bruce A.},
  month = sep,
  year = {1970},
  pages = {367-382},
  file = {/home/kazeiv/Zotero/storage/VM2MPLPR/Bolt_1970_PdP and PKiKP Waves and Diffracted PcP Waves.pdf;/home/kazeiv/Zotero/storage/NNECQST3/abstract.html}
}

@article{zhou2015,
  title = {Full Waveform Inversion of Diving \& Reflected Waves for Velocity Model Building with Impedance Inversion Based on Scale Separation},
  volume = {202},
  doi = {10.1093/gji/ggv228},
  abstract = {Full waveform inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, post-critical reflections and short-spread reflections. Most successful applications of FWI are driven by the information carried by diving waves and post-critical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches, referred to as reflection waveform inversion (RWI), have been recently revisited to retrieve these long-to-intermediate wavelengths from short-spread reflections by using some prior knowledge of the reflectivity and a scale separation between the velocity macromodel and the reflectivity. This study presents a unified formalism of FWI, named as Joint FWI, whose aim is to efficiently combine the diving and reflected waves for velocity model building. The two key ingredients of Joint FWI are, on the data side, the explicit separation between the short-spread reflections and the wide-angle arrivals and, on the model side, the scale separation between the velocity macromodel and the short-scale impedance model. The velocity model and the impedance model are updated in an alternate way by Joint FWI and waveform inversion of the reflection data (least-squares migration), respectively. Starting from a crude velocity model, Joint FWI is applied to the streamer seismic data computed in the synthetic Valhall model. While the conventional FWI is stuck into a local minimum due to cycle skipping, Joint FWI succeeds in building a reliable velocity macromodel. Compared with RWI, the use of diving waves in Joint FWI improves the reconstruction of shallow velocities, which translates into an improved imaging at deeper depths. The smooth velocity model built by Joint FWI can be subsequently used as a reliable initial model for conventional FWI to increase the high-wavenumber content of the velocity model.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Zhou, Wei and Brossier, Romain and Operto, Stephane and Virieux, Jean},
  year = {2015},
  pages = {1535-1554},
  eprint = {http://gji.oxfordjournals.org/content/202/3/1535.full.pdf+html}
}

@book{cerveny2001seismic,
  title = {Seismic Ray Theory},
  publisher = {{Cambridge}},
  author = {\v{}Cerven\'y, V.},
  year = {2001}
}

@article{bunks1995,
  title = {Multiscale Seismic Waveform Inversion},
  volume = {60},
  doi = {10.1190/1.1443880},
  abstract = {Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low-frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.},
  number = {5},
  journal = {Geophysics},
  author = {Bunks, Carey and Saleck, Fatimetou M. and Zaleski, S. and Chavent, G.},
  year = {1995},
  pages = {1457-1473},
  eprint = {http://geophysics.geoscienceworld.org/content/60/5/1457.full.pdf+html}
}

@article{alkhalifah2015full,
  title = {Full Model Wavenumber Inversion},
  volume = {2015},
  number = {1},
  journal = {ASEG Extended Abstracts},
  author = {Alkhalifah, Tariq A},
  year = {2015},
  pages = {1-1},
  publisher = {{CSIRO}}
}

@article{ref:kuvshinov,
  title = {The Exact Solution of the Time-Harmonic Wave Equation for a Linear Velocity Profile},
  volume = {167},
  doi = {10.1111/j.1365-246X.2006.03194.x},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Kuvshinov, B. N. and Mulder, W. A.},
  year = {2006},
  pages = {659-662}
}

@article{ref:pratt99,
  title = {Two-Dimensional Velocity Models from Wide-Angle Seismic Data by Waveform Inversion},
  volume = {124},
  doi = {10.1111/j.1365-246X.1996.tb07023.x},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Pratt, R[] G[] and Song, Z.-M and Williamson, P[] R[] and Warner, M[] R[]},
  year = {1996},
  pages = {323-340}
}

@article{pekeris:295,
  title = {Theory of {{Propagation}} of {{Sound}} in a {{Half}}-{{Space}} of {{Variable Sound Velocity}} under {{Conditions}} of {{Formation}} of a {{Shadow Zone}}},
  volume = {18},
  doi = {10.1121/1.1916366},
  number = {2},
  journal = {The Journal of the Acoustical Society of America},
  author = {Pekeris, C. L.},
  year = {1946},
  pages = {295-315},
  publisher = {{ASA}}
}

@book{ref:troyan,
  title = {Analysis and Processing of Data},
  publisher = {{St. Petersburg State University Press}},
  author = {Troyan, V[] N[] and Kiselev, Yuri V[]},
  year = {2010},
  note = {(in Russian)}
}

@techreport{ref:babich,
  title = {About the {{Smirnov}}-{{Sobolev}} Method for the Explicit Solution of the Problems of Mathematical Physics},
  author = {Babich, V[] M[] and Kochuguev, S[] K[]},
  howpublished = {Steklov Mathematical Institute, St. Petersburg},
  note = {(in Russian)}
}

@book{ref:chervenyheadwaves,
  title = {Theory of Seismic Head Waves},
  publisher = {{University of Toronto Press}},
  author = {\v{}Cerven\'y, Vlastislav and Ravindra, Ravi},
  year = {1971},
  urlx = {http://seis.karlov.mff.cuni.cz/papers.bin/a71vc1.pdf}
}

@article{wu:11,
  title = {Diffraction Tomography and Multisource Holography Applied to Seismic Imaging},
  volume = {52},
  doi = {10.1190/1.1442237},
  number = {1},
  journal = {Geophysics},
  author = {Wu, R.S. and Toks\"oz, M.N.},
  year = {1987},
  pages = {11-25},
  publisher = {{SEG}},
  urlx = {http://link.aip.org/link/?GPY/52/11/1}
}

@article{mora1989,
  title = {Inversion = Migration + Tomography},
  volume = {54},
  doi = {10.1190/1.1442625},
  number = {12},
  journal = {Geophysics},
  author = {Mora, Peter},
  year = {1989},
  pages = {1575-1586},
  publisher = {{SEG}},
  urlx = {http://link.aip.org/link/?GPY/54/1575/1}
}

@book{ref:akirichards,
  title = {Quantitative Seismology: {{Theory}} and Methods, {{Volume}} 1},
  publisher = {{Freeman, San Francisco}},
  author = {Aki, K[] and Richards, P[] G[]},
  year = {1980}
}

@article{Mulder,
  title = {Exploring Some Issues in Acoustic Full Waveform Inversion},
  volume = {56},
  issn = {1365-2478},
  doi = {10.1111/j.1365-2478.2008.00708.x},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Mulder, W. A. and Plessix, R.-\'E.},
  year = {2008},
  pages = {827-841},
  publisher = {{Blackwell Publishing Ltd}}
}

@article{devaney1984,
  title = {Geophysical {{Diffraction Tomography}}},
  volume = {GE-22},
  doi = {10.1109/TGRS.1984.350573},
  number = {1},
  journal = {IEEE Transactions on Geoscience and Remote Sensing},
  author = {Devaney, A. J.},
  month = jan,
  year = {1984},
  pages = {3-13},
  xissn = {0196-2892}
}

@article{gupta:122,
  title = {Reflection of Plane Waves from a Linear Transition Layer in Liquid Media},
  volume = {30},
  doi = {10.1190/1.1439528},
  number = {1},
  journal = {Geophysics},
  author = {Gupta, Ravindra N.},
  year = {1965},
  pages = {122-132},
  publisher = {{SEG}}
}

@article{Dunster,
  title = {{{BEssel Functions}} of {{Purely Imaginary Order}}, with an {{Application}} to {{Second}}-{{Order Linear Differential Equations Having}} a {{Large Parameter}}},
  volume = {21},
  doi = {10.1137/0521055},
  number = {4},
  journal = {SIAM Journal on Mathematical Analysis},
  author = {Dunster, T.},
  year = {1990},
  pages = {995-1018},
  eprint = {http://epubs.siam.org/doi/pdf/10.1137/0521055}
}

@article{iturraran-viverosValidatedArtificialNeural2018,
  title = {Validated Artificial Neural Networks in Determining Petrophysical Properties: {{A}} Case Study from {{Colombia}}},
  volume = {6},
  issn = {2324-8858},
  shorttitle = {Validated Artificial Neural Networks in Determining Petrophysical Properties},
  doi = {10.1190/INT-2018-0011.1},
  abstract = {We have applied instantaneous seismic attributes to a stacked P-wave reflected seismic section in the Tenerife field located in the Middle Magdalena Valley Basin in Colombia to estimate the volume of clay VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and the density {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$} at seismic scale. The well logs and the seismic attributes associated to the seismic trace closer to one of the available wells (Tenerife-2) is the information used to train some multilayered artificial neural networks (ANN). We perform data analysis via the gamma test, a mathematically nonparametric nonlinear smooth modeling tool, to choose the best input combination of seismic attributes to train ANNs to estimate VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$}. Once the ANNs are trained, they are applied to predict these parameters along the seismic line. From the continuous estimations of VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$}, we distinguish two facies: sands for Vclay{$<$}0.5Vclay{$<$}0.5{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}mo{$>\&$}lt;{$<$}/mo{$><$}mn{$>$}0.5{$<$}/mn{$><$}/mrow{$><$}/math{$>$} and shales when Vclay{$\geq$}0.5Vclay{$\geq$}0.5{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}mo{$>\geq{}<$}/mo{$><$}mn{$>$}0.5{$<$}/mn{$><$}/mrow{$><$}/math{$>$}. These estimations confirm the production of the Mugrosa C-Sands zone, and we draw the brown shale that correlates with the high-amplitude attributes and the yellow sand that correlates with the low-amplitude attributes. Using the well-log information for VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and the facies classification (also in the well log), two cubic polynomials that depend on time (or depth) are obtained, one for sands and the other for shales, to fit the VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$}. These two cubic polynomials and the facies classification obtained from the VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} at the seismic scale enable us to estimate VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} at the seismic scale. To validate the 2D VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$} predicted data, a forward-modeling software (the Kennett reflectivity algorithm) is used. This model calculates synthetic seismograms that are compared with the real seismograms. This comparison indicates a small misfit that suggests that the VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$} images are representing the reservoir description characteristics and the ANN method is accurate to map these parameters.},
  number = {4},
  journal = {Interpretation},
  author = {{Iturrar\'an-Viveros}, Ursula and {Mu\~noz-Garc\'ia}, Andr\'es M. and Parra, Jorge O. and Tago, Josu\'e},
  month = aug,
  year = {2018},
  pages = {T1067-T1080},
  file = {/home/kazeiv/Zotero/storage/X28EJM5U/Iturrarán-Viveros et al. - 2018 - Validated artificial neural networks in determinin.html}
}

@article{boieroSwaveSplittingIntensity2019,
  title = {S-Wave Splitting Intensity Analysis and Inversion},
  volume = {67},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12729},
  abstract = {Analysing S-wave splitting has become a routine step in processing multicomponent data. Typically, this analysis leads to determining the principal directions of a transversely isotropic medium with a horizontal symmetry axis, which is assumed to be responsible for azimuthal anisotropy, and to the time delays between the fast and slow S-waves. These parameters are commonly estimated layer-by-layer from the top. Errors in layer stripping occurring in shallow layers might propagate to deeper layers. We propose a method for S-wave splitting analysis and compensation that consists of inverting interval values of splitting intensity to obtain a model of anisotropic parameters that vary with time and/or depth. Splitting intensity is a robust attribute with respect to structural variations and is commutative, which means that it can be summed along a ray (or throughout a sensitivity kernel volume) and can be linearly related to anisotropic perturbations at depth. Therefore, it is possible to estimate anisotropic properties within a geological formation (e.g. the reservoir) by analysing the differences of splitting intensity measured at the top and at the bottom of the layer. This allows us to avoid layer stripping, in particular, for shallow layers where anisotropic parameters are difficult to estimate due to poor coverage, and it makes S-wave splitting analysis simpler to apply. We demonstrate this method on synthetic and real data. Because the splitting intensity attribute shows usefulness in S-wave splitting analysis in transversely isotropic media, we extend the splitting intensity theory to lower symmetry classes. It enables the characterization of tilted transversely isotropic and tilted orthorhombic media, opening new opportunities for anisotropic model building.},
  language = {English},
  number = {2},
  journal = {Geophysical Prospecting},
  author = {Boiero, D. and Bagaini, C.},
  month = feb,
  year = {2019},
  pages = {362-378},
  file = {/home/kazeiv/Zotero/storage/LGQFM4BB/Boiero and Bagaini - 2019 - S-wave splitting intensity analysis and inversion.pdf}
}

@article{liDeepEarthquakesSubducting2018,
  title = {Deep Earthquakes in Subducting Slabs Hosted in Highly Anisotropic Rock Fabric},
  volume = {11},
  issn = {1752-0894, 1752-0908},
  doi = {10.1038/s41561-018-0188-3},
  language = {en},
  number = {9},
  journal = {Nature Geoscience},
  author = {Li, Jiaxuan and Zheng, Yingcai and Thomsen, Leon and Lapen, Thomas J. and Fang, Xinding},
  month = sep,
  year = {2018},
  pages = {696-700},
  file = {/home/kazeiv/Zotero/storage/RU8M39DH/Li et al. - 2018 - Deep earthquakes in subducting slabs hosted in hig.pdf}
}

@article{kazeiScatteringRadiationPattern2019,
  title = {Scattering {{Radiation Pattern Atlas}}: {{What}} Anisotropic Elastic Properties Can Body Waves Resolve?},
  journal = {JGR Solid Earth (submitted)},
  author = {Kazei, Vladimir and Alkhalifah, Tariq},
  year = {2019}
}

@article{alkhalifahVelocityAnalysisTransversely1995,
  title = {Velocity Analysis for Transversely Isotropic Media},
  volume = {60},
  number = {5},
  journal = {Geophysics},
  author = {Alkhalifah, Tariq and Tsvankin, Ilya},
  year = {1995},
  pages = {1550-1566}
}

@article{mobilenet,
  title = {Mobilenets: {{Efficient}} Convolutional Neural Networks for Mobile Vision Applications},
  journal = {arXiv preprint arXiv:1704.04861},
  author = {Howard, Andrew G. and Zhu, Menglong and Chen, Bo and Kalenichenko, Dmitry and Wang, Weijun and Weyand, Tobias and Andreetto, Marco and Adam, Hartwig},
  year = {2017}
}

@article{EZW,
  title = {Hyperspectral Image Compression: Adapting {{SPIHT}} and {{EZW}} to Anisotropic 3-{{D}} Wavelet Coding},
  volume = {17},
  number = {12},
  journal = {IEEE Transactions on Image processing},
  author = {Christophe, Emmanuel and Mailhes, Corinne and Duhamel, Pierre},
  year = {2008},
  pages = {2334-2346}
}

@inproceedings{aravkinNonlinearSparsityPromoting2011,
  title = {A Nonlinear Sparsity Promoting Formulation and Algorithm for Full Waveform Inversion},
  isbn = {2214-4609},
  booktitle = {73rd {{EAGE Conference}} and {{Exhibition}} Incorporating {{SPE EUROPEC}} 2011},
  author = {Aravkin, A. Y. and Van Leeuwen, Tristan and Burke, James V. and Herrmann, F. J.},
  year = {2011}
}

@article{kaplan2017,
  title = {Low Frequency Full Waveform Seismic Inversion within a Tree Based {{Bayesian}} Framework},
  volume = {212},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Ray, Anandaroop and Kaplan, Sam and Washbourne, John and Albertin, Uwe},
  year = {2017},
  pages = {522-542}
}

@article{jpeg2000,
  title = {{{JPEG2000}}: {{Standard}} for Interactive Imaging},
  volume = {90},
  number = {8},
  journal = {Proceedings of the IEEE},
  author = {Taubman, David S. and Marcellin, Michael W.},
  year = {2002},
  pages = {1336-1357}
}

@article{laineTextureClassificationWavelet1993,
  title = {Texture Classification by Wavelet Packet Signatures},
  volume = {15},
  number = {11},
  journal = {IEEE Transactions on pattern analysis and machine intelligence},
  author = {Laine, Andrew and Fan, Jian},
  year = {1993},
  pages = {1186-1191}
}

@article{polo2018,
  title = {Deep-Learning Tomography},
  volume = {37},
  number = {1},
  journal = {The Leading Edge},
  author = {{Araya-Polo}, Mauricio and Jennings, Joseph and Adler, Amir and Dahlke, Taylor},
  year = {2018},
  pages = {58-66}
}

@book{db1992,
  title = {Ten Lectures on Wavelets},
  volume = {61},
  isbn = {1-61197-010-5},
  publisher = {{Siam}},
  author = {Daubechies, Ingrid},
  year = {1992}
}

@incollection{linSeismicFullwaveformInversion2012,
  title = {Seismic Full-Waveform Inversion Using Truncated Wavelet Representations},
  isbn = {1052-3812},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2012},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Lin, Y. and Abubakar, A. and Habashy, T. M.},
  year = {2012},
  pages = {1-6}
}

@inproceedings{liNeuralNetworksAid1998,
  title = {Neural Networks as an Aid to Iterative Optimization Methods},
  volume = {2},
  isbn = {0-7803-4778-1},
  booktitle = {{{SMC}}'98 {{Conference Proceedings}}. 1998 {{IEEE International Conference}} on {{Systems}}, {{Man}}, and {{Cybernetics}} ({{Cat}}. {{No}}. {{98CH36218}})},
  publisher = {{IEEE}},
  author = {Li, H. J. and Sung, Andrew H. and Weiss, William W. and Wo, S. C.},
  year = {1998},
  pages = {1812-1817}
}

@article{zhangVelocityGANDataDrivenFullWaveform2018,
  title = {{{VelocityGAN}}: {{Data}}-{{Driven Full}}-{{Waveform Inversion Using Conditional Adversarial Networks}}},
  journal = {arXiv preprint arXiv:1809.10262},
  author = {Zhang, Zhongping and Wu, Yue and Lin, Youzuo and Zhou, Zheng},
  year = {2018}
}

@incollection{wuInversionNetAccurateEfficient2018,
  title = {{{InversionNet}}: {{Accurate}} and Efficient Seismic Waveform Inversion with Convolutional Neural Networks},
  isbn = {1949-4645},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Wu, Yue and Lin, Youzuo and Zhou, Zheng},
  year = {2018},
  pages = {2096-2100}
}

@article{fanInverseNetSolvingInverse2017,
  title = {{{InverseNet}}: {{Solving Inverse Problems}} with {{Splitting Networks}}},
  journal = {arXiv preprint arXiv:1712.00202},
  author = {Fan, Kai and Wei, Qi and Wang, Wenlin and Chakraborty, Amit and Heller, Katherine},
  year = {2017}
}

@incollection{sunLowFrequencyExtrapolation2018,
  title = {Low Frequency Extrapolation with Deep Learning},
  isbn = {1949-4645},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Sun, Hongyu and Demanet, Laurent},
  year = {2018},
  pages = {2011-2015}
}

@inproceedings{ovcharenkoLowFrequencyDataExtrapolation2018,
  title = {Low-{{Frequency Data Extrapolation Using}} a {{Feed}}-{{Forward ANN}}},
  isbn = {2214-4609},
  booktitle = {80th {{EAGE Conference}} and {{Exhibition}} 2018},
  author = {Ovcharenko, Oleg and Kazei, Vladimir and Peter, Daniel and Zhang, Xiangliang and Alkhalifah, Tariq},
  year = {2018}
}

@inproceedings{ovcharenkoNeuralNetworkBased2017,
  title = {Neural Network Based Low-Frequency Data Extrapolation},
  booktitle = {3rd {{SEG FWI}} Workshop: {{What}} Are We Getting},
  author = {Ovcharenko, Oleg and Kazei, Vladimir and Peter, Daniel and Alkhalifah, T.},
  year = {2017}
}

@article{ivanovNormalModesOrthorhombic2018,
  title = {Normal Modes in Orthorhombic Media},
  doi = {10.1093/gji/ggy534},
  abstract = {SUMMARY.  Guided waves in a water layer overlaying an elastic half-space are known as normal modes. They are often present in seismic recordings at long offsets},
  language = {en},
  journal = {Geophysical Journal International},
  author = {Ivanov, Yuriy and Stovas, Alexey and Kazei, Vladimir},
  year = {2018},
  file = {/home/kazeiv/Zotero/storage/QB9ARUZ3/Ivanov et al. - Normal modes in orthorhombic media.pdf}
}

@article{mulderExploringIssuesAcoustic2008,
  title = {Exploring Some Issues in Acoustic Full Waveform Inversion},
  volume = {56},
  copyright = {\textcopyright{} Shell International Exploration and Production B.V.},
  issn = {1365-2478},
  doi = {10.1111/j.1365-2478.2008.00708.x},
  abstract = {The least-squares error measures the difference between observed and modelled seismic data. Because it suffers from local minima, a good initial velocity model is required to avoid convergence to the wrong model when using a gradient-based minimization method. If a data set mainly contains reflection events, it is difficult to update the velocity model with the least-squares error because the minimization method easily ends up in the nearest local minimum without ever reaching the global minimum. Several authors observed that the model could be updated by diving waves, requiring a wide-angle or large-offset data set. This full waveform tomography is limited to a maximum depth. Here, we use a linear velocity model to obtain estimates for the maximum depth. In addition, we investigate how frequencies should be selected if the seismic data are modelled in the frequency domain. In the presence of noise, the condition to avoid local minima requires more frequencies than needed for sufficient spectral coverage. We also considered acoustic inversion of a synthetic marine data set created by an elastic time-domain finite-difference code. This allowed us to validate the estimates made for the linear velocity model. The acoustic approximation leads to a number of problems when using long-offset data. Nevertheless, we obtained reasonable results. The use of a variable density in the acoustic inversion helped to match the data at the expense of accuracy in the inversion result for the density.},
  language = {en},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Mulder, W. A. and Plessix, R.-E.},
  year = {2008},
  pages = {827-841}
}

@inproceedings{kazeiSaltbodyInversionMinimum2017,
  title = {Salt-Body {{Inversion}} with {{Minimum Gradient Support}} and {{Sobolev Space Norm Regularizations}}},
  doi = {10.3997/2214-4609.201700600},
  abstract = {Full-waveform inversion (FWI) is a technique which solves the ill-posed seismic inversion problem of fitting our model data to the measured ones from the field. FWI is capable of providing high-resolution estimates of the model, and of handling wave propagation of arbitrary complexity (visco-elastic, anisotropic); yet, it often fails to retrieve high-contrast geological structures, such as salt. One of the reasons for the FWI failure is that the updates at earlier iterations are too smooth to capture the sharp edges of the salt boundary. We compare several regularization approaches, which promote sharpness of the edges. Minimum gradient support (MGS) regularization focuses the inversion on blocky models, even more than the total variation (TV) does. However, both approaches try to invert undesirable high wavenumbers in the model too early for a model of complex structure. Therefore, we apply the Sobolev space norm as a regularizing term in order to maintain a balance between sharp and smooth updates in FWI. We demonstrate the application of these regularizations on a Marmousi model, enriched by a chunk of salt. The model turns out to be too complex in some parts to retrieve its full velocity distribution, yet the salt shape and contrast are retrieved.},
  language = {English},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Kazei, Vladimir and Kalita, M. and Alkhalifah, T.},
  month = jun,
  year = {2017},
  file = {/home/kazeiv/Zotero/storage/JV8FRPGI/Kazei et al. - 2017 - Salt-body Inversion with Minimum Gradient Support .pdf}
}

@article{esserTotalvariationRegularizationStrategies2016,
  title = {Total-Variation Regularization Strategies in Full-Waveform Inversion},
  language = {en},
  journal = {arxiv.org},
  author = {Esser, Ernie and Guasch, Lluis and {van Leeuwen}, Tristan and Aravkin, Aleksandr Y. and Herrmann, Felix J.},
  month = aug,
  year = {2016},
  file = {/home/kazeiv/Zotero/storage/2S3RANB2/Esser et al. - 2016 - Total-variation regularization strategies in full-.pdf}
}

@article{shawUseAVOAData2006,
  title = {Use of {{AVOA}} Data to Estimate Fluid Indicator in a Vertically Fractured Medium},
  volume = {71},
  issn = {0016-8033},
  doi = {10.1190/1.2194896},
  abstract = {Microstructural attributes of cracks and fractures, such as crack density, aspect ratio, and fluid infill, determine the elastic properties of a medium containing a set of parallel, vertical fractures. Although the tangential weakness  {$\Delta$}T{$\Delta$}T{$<$}math display="inline" overflow="scroll"{$><$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}T{$<$}/mi{$><$}/msub{$><$}/math{$>$}  of the fractures does not vary with the fluid content, the normal weakness  {$\Delta$}N{$\Delta$}N{$<$}math display="inline" overflow="scroll"{$><$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}N{$<$}/mi{$><$}/msub{$><$}/math{$>$}  exhibits significant dependence on fluid infill. Based on linear-slip theory, we used the ratio  g{$\Delta$}N{$\slash\Delta$}Tg{$\Delta$}N{$\slash\Delta$}T{$<$}math display="inline" overflow="scroll"{$>$} {$<$}mrow{$><$}mi{$>$}g{$<$}/mi{$>$} {$<$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}N{$<$}/mi{$><$}/msub{$>$} {$<$}mo{$>\slash{}<$}/mo{$>$} {$<$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}T{$<$}/mi{$><$}/msub{$>$} {$<$}/mrow{$>$} {$<$}/math{$>$}  \textemdash{} termed the fluid indicator \textemdash{} as a quantitative measure of the fluid content in the fractures, with g representing the square of the ratio of S- and P-wave velocity in the unfractured medium. We used a Born formalism to derive the sensitivity to fracture weakness of PP- and PS-reflection coefficients for an interface separating an unfractured medium from a vertically fractured medium. Our formulae reveal that the PP-reflection coefficient does not depend on the 2D microcorrugation/surface roughness with ridges and valleys parallel to the fracture strike, whereas the PS-reflection coefficient is sensitive to this microstructural property of the fractures. Based on this formulation, we developed a method to compute the fluid indicator from wide-azimuth PP-AVOA data. Inversion of synthetic data corrupted with 10\% random noise reliably estimates the normal and tangential fracture weaknesses and hence the fluid indicator can be determined accurately when the fractures are liquid-filled or partially saturated. As the gas saturation in the fractures increases, the quality of inversion becomes poorer. Errors of 15\%\textendash{}20\% in g do not affect the estimation of fluid indicator significantly in case of liquid infill or partial saturation. However, for gas-saturated fractures, incorrect values of g may have a significant effect on fluid-indicator estimates.},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Shaw, R. and Sen, M.},
  month = may,
  year = {2006},
  pages = {C15-C24},
  file = {/home/kazeiv/Zotero/storage/UCHIDZLI/Shaw and Sen - 2006 - Use of AVOA data to estimate fluid indicator in a .pdf}
}

@article{naeiniMainComponentsFullwaveform2016,
  title = {Main Components of Full-Waveform Inversion for Reservoir Characterization},
  volume = {34},
  issn = {1365-2397},
  doi = {10.3997/1365-2397.2016015},
  abstract = {Building a 3D reservoir model, which has become a key part of reservoir management, is a challenging task. Classic seismic inversion techniques, both deterministic and stochastic, have attempted to reduce the uncertainty in reservoir modelling. However, these inversion methods are typically based just on amplitude and make a number of critical simplifying assumptions, such as that migrated data are accurate and can be modelled by 1D convolution (using reflection coefficients computed from the Zoeppritz equation or its linear approximations). Migration algorithms themselves may suffer from inadequate amplitude and multiple-scattering treatments. Full-waveform inversion (FWI), specifically designed for the direct estimation of the reservoir parameters, is proposed here as an alternative method for seismic reservoir characterization. This is clearly an ambitious goal, and it is not our intention to claim we have already achieved it. Instead, we intend to introduce the main components of such reservoir-oriented inversion and discuss a strategy for elastic, anisotropic FWI constrained by rockphysics models and facies types. Among the many challenges, we focus mostly on understanding the physics and describing some elements of an efficient forward-modelling engine. In particular, we show how analysing the radiation patterns helps to optimise the parameterisation and could reduce the null space.},
  language = {en},
  number = {2141},
  journal = {First Break},
  author = {Naeini, Ehsan Zabihi and Alkhalifah, Tariq and Tsvankin, Ilya and Kamath, Nishant and Cheng, Jiubing},
  month = nov,
  year = {2016},
  file = {/home/kazeiv/Zotero/storage/PBBYGBWI/Naeini et al. - 2016 - Main components of full-waveform inversion for res.pdf}
}

@article{vidaleFinescaleHeterogeneityEarth2000,
  title = {Fine-Scale Heterogeneity in the {{Earth}}'s Inner Core},
  volume = {404},
  issn = {0028-0836, 1476-4687},
  doi = {10.1038/35005059},
  language = {en},
  number = {6775},
  journal = {Nature},
  author = {Vidale, John E. and Earle, Paul S.},
  month = mar,
  year = {2000},
  pages = {273-275},
  file = {/home/kazeiv/Zotero/storage/K2JIK96S/Vidale and Earle - 2000 - Fine-scale heterogeneity in the Earth's inner core.pdf}
}

@article{masmoudiFullwaveformInversionAcoustic2018,
  title = {Full-Waveform Inversion in Acoustic Orthorhombic Media and Application to a {{North Sea}} Data Set},
  volume = {83},
  issn = {0016-8033},
  doi = {10.1190/geo2017-0738.1},
  abstract = {Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.},
  number = {5},
  journal = {GEOPHYSICS},
  author = {Masmoudi, N. and Alkhalifah, T.},
  month = jun,
  year = {2018},
  pages = {C179-C193},
  file = {/home/kazeiv/Zotero/storage/FGDWBFI9/Masmoudi and Alkhalifah - 2018 - Full-waveform inversion in acoustic orthorhombic m.pdf}
}

@article{gholamiWhichParameterizationSuitable2013,
  title = {Which Parameterization Is Suitable for Acoustic Vertical Transverse Isotropic Full Waveform Inversion? {{Part}} 1: {{Sensitivity}} and Trade-off Analysis},
  volume = {78},
  issn = {0016-8033},
  shorttitle = {Which Parameterization Is Suitable for Acoustic Vertical Transverse Isotropic Full Waveform Inversion?},
  doi = {10.1190/geo2012-0204.1},
  abstract = {In most geologic environments, accounting for anisotropy is necessary to perform acoustic full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data because of the potential dependence of wave speeds on the direction of the wave propagation. In the framework of multiparameter FWI, the subsurface parameterization controls the influence of the different parameter classes on the modeled seismic data as a function of the scattering angle and hence the resolution with which the parameters can be reconstructed and the potential trade-off between different parameters. We have evaluated a numerical procedure based on computation of the scattering patterns of the different parameters to assess the sensitivity of the seismic data to different parameterizations of vertical transverse isotropic media in the acoustic approximation. Among the different categories we have tested, a monoparametric FWI was found for imaging one wave speed with a broad wavenumber content, keeping the Thomsen parameters fixed, which have a small influence on the data relative to the wave speed. This raises the question of the initial information required in the background models of the Thomsen parameters to perform reliable monoparameter FWI. Alternatively, simultaneously inverting the horizontal and vertical wave speeds introduces limited trade-off effects because these wave speeds have significant influence on the data for distinct ranges of scattering angles, while the influence of the Thomsen parameter {$\delta\delta{}<$}math display="inline" overflow="scroll"{$><$}mi{$>\delta{}<$}/mi{$><$}/math{$>$} remains weak. With such parameterization, the short-to-intermediate wavelengths of the vertical velocity are updated from the short-to-intermediate scattering angles, while the long-to-intermediate wavelengths of the horizontal velocity are updated from the wide-to-intermediate scattering angles. We concluded that the choice of the subsurface parameterization can be driven by the acquisition geometry, which controls the scattering-angle coverage and hence the resolving power of FWI, and by the accuracy of the available initial FWI models.},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Gholami, Y. and Brossier, R. and Operto, S. and Ribodetti, A. and Virieux, J.},
  month = mar,
  year = {2013},
  pages = {R81-R105},
  file = {/home/kazeiv/Zotero/storage/CPP2XIB6/Gholami et al. - 2013 - Which parameterization is suitable for acoustic ve.pdf}
}

@article{cheverdaRpseudoinversesCompactOperators1995,
  title = {R-Pseudoinverses for Compact Operators in {{Hilbert}} Spaces: Existence and Stability},
  volume = {3},
  number = {2},
  journal = {Journal of Inverse and Ill-Posed Problems},
  author = {Cheverda, V. A. and Kostin, V. I.},
  year = {1995},
  pages = {131-148}
}

@article{cheverdaRpseudoinversesCompactOperators2009,
  title = {R-Pseudoinverses for Compact Operators in {{Hilbert}} Spaces: Existence and Stability},
  volume = {3},
  issn = {1569-3945},
  shorttitle = {R-Pseudoinverses for Compact Operators in {{Hilbert}} Spaces},
  doi = {10.1515/jiip.1995.3.2.131},
  number = {2},
  journal = {Journal of Inverse and Ill-Posed Problems},
  author = {CHEVERDA, V. A. and KOSTIN, V. I.},
  year = {2009},
  pages = {131--148}
}

@article{schusterFarfieldSuperresolutionImaging2014,
  title = {Far-Field Superresolution by Imaging of Resonant Multiples},
  volume = {199},
  issn = {0956-540X},
  doi = {10.1093/gji/ggu350},
  abstract = {Summary.  We show that superresolution imaging in the far-field region of the sources and receivers is theoretically and practically possible if migration of re},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Schuster, Gerard T. and Huang, Yunsong},
  month = dec,
  year = {2014},
  pages = {1943-1949},
  file = {/home/kazeiv/Zotero/storage/7PLIXQ4B/Schuster and Huang - 2014 - Far-field superresolution by imaging of resonant m.pdf}
}

@article{raknes2014,
  title = {Time-Lapse Full-Waveform Inversion of Limited-Offset Seismic Data Using a Local Migration Regularization},
  volume = {79},
  number = {3},
  journal = {Geophysics},
  author = {Raknes, Espen Birger and Arntsen, B\o{}rge},
  year = {2014},
  pages = {WA117-WA128},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{podgornovaResolutionVTIAnisotropy2018,
  title = {Resolution of {{VTI}} Anisotropy with Elastic Full-Waveform Inversion: Theory and Basic Numerical Examples},
  issn = {0956-540X},
  doi = {10.1093/gji/ggy116},
  abstract = {Extracting medium properties from seismic data faces some limitations due to the finite frequency content of the data and restricted spatial positions of the sources and receivers. Some distributions of the medium properties make low impact on the data (including none). If these properties are used as the inversion parameters, then the inverse problem becomes over-parametrized, leading to ambiguous results. We present an analysis of multiparameter resolution for the linearized inverse problem in the framework of elastic full-waveform inversion. We show that the spatial and multiparameter sensitivities are intertwined and non-sensitive properties are spatial distributions of some non-trivial combinations of the conventional elastic parameters. The analysis accounts for the Hessian information and frequency content of the data; it is semi-analytical (in some scenarios analytical), easy to interpret, and enhances results of the widely used radiation pattern analysis. Single-type scattering is shown to have limited sensitivity, even for full-aperture data. Finite-frequency data lose multiparameter sensitivity at smooth and fine spatial scales. Also, we establish ways to quantify a spatial-multiparameter coupling and demonstrate that the theoretical predictions agree well with the numerical results.},
  journal = {Geophysical Journal International},
  author = {Podgornova, O and Leaney, S and Liang, L},
  month = mar,
  year = {2018},
  pages = {ggy116-ggy116}
}

@article{snieder3DLinearizedScattering1986,
  title = {3-{{D}} Linearized Scattering of Surface Waves and a Formalism for Surface Wave Holography},
  volume = {84},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.1986.tb04372.x},
  abstract = {Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine-like crustal structure. Furthermore a `great circle theorem' in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter-space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do `surface wave holography'.},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Snieder, Roel},
  month = mar,
  year = {1986},
  pages = {581-605},
  file = {/home/kazeiv/Zotero/storage/G32I56CG/Snieder - 1986 - 3-D linearized scattering of surface waves and a f.pdf;/home/kazeiv/Zotero/storage/QM8HKTYZ/Snieder_1986_3-D linearized scattering of surface waves and a formalism for surface wave.pdf}
}

@incollection{kalitaRegularizedFullwaveformInversion2018,
  series = {{{SEG Technical Program Expanded Abstracts}}},
  title = {Regularized Full-Waveform Inversion for Salt Bodies},
  abstract = {Full-waveform inversion (FWI) aims to resolve an ill-posed non-linear optimization problem in order to retrieve unknown subsurface model parameters with high resolution from seismic data. The non-linearity, in the absence of low frequencies from the recorded seismic signal, tends to increase, especially for large-velocity structures, like salt bodies and the sediments beneath them, and often prevents the inversion from obtaining an adequate model. To alleviate the ill-posedness of FWI for salt-bodies, we propose to utilize model regularization in order to promote a limited variation in the inverted model and a salt-flooding regularization from the top of the salt (without picking). On that account, we split the optimization problem into two parts: first, we minimize the data misfit and the total variation in the model, seeking to achieve an inverted model with sharp interfaces; and second, we penalize sharp velocity drops in the model by a computational flooding of the velocity field. Unlike conventional industrial salt flooding, our proposed technique requires minimal human intervention and no information whatsoever about the top of the salt. Those features are demonstrated on a dataset of the Sigsbee2A model in which the lowest available frequency is 3~Hz. We retrieve most of the salt region and also some of the fine sedimentary layering beneath the salt.Presentation Date: Monday, October 15, 2018Start Time: 1:50:00 PMLocation: 207C (Anaheim Convention Center)Presentation Type: Oral},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Kalita, M. and Kazei, V. and Choi, Y. and Alkhalifah, T.},
  month = aug,
  year = {2018},
  pages = {1043-1047},
  doi = {10.1190/segam2018-2995963.1}
}

@article{alkhalifahFullmodelWavenumberInversion2016,
  title = {Full-Model Wavenumber Inversion: {{An}} Emphasis on the Appropriate Wavenumber Continuation},
  volume = {81},
  issn = {0016-8033},
  shorttitle = {Full-Model Wavenumber Inversion},
  doi = {10.1190/geo2015-0537.1},
  abstract = {A model of the earth can be described using a Fourier basis represented by its wavenumber content. In full-waveform inversion (FWI), the wavenumber description of the model is natural because our Born-approximation-based velocity updates are made up of wavefields. Our objective in FWI is to access all the model wavenumbers available in our limited aperture and bandwidth recorded data that are not yet accurately present in the initial velocity model. To invert for those model wavenumbers, we need to locate their imprint in the data. Thus, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identified their individual influence on the data. Missing the energy for a single vertical low-model wavenumber from the residual between the true Marmousi model and some initial linearly increasing velocity model produced a worse least-squares fit to the data than the initial model itself, in which all the residual model wavenumbers were missing. This stern realization validated the importance of wavenumber continuation, specifically starting from the low-model wavenumbers, to higher (resolution) wavenumbers, especially those attained in an order dictated by the scattering angle filter. A numerical Marmousi example determined the important role that the scattering angle filter played in managing the wavenumber continuation from low to high. An application on the SEG2014 blind test data set with frequencies lower than 7~Hz muted out further validated the versatility of the scattering angle filtering.},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Alkhalifah, T.},
  month = apr,
  year = {2016},
  pages = {R89-R98},
  file = {/home/kazeiv/Zotero/storage/QGYB89PR/Alkhalifah - 2016 - Full-model wavenumber inversion An emphasis on th.pdf}
}

@article{opertoEfficient3DFrequencydomain2015,
  title = {Efficient 3-{{D}} Frequency-Domain Mono-Parameter Full-Waveform Inversion of Ocean-Bottom Cable Data: Application to {{Valhall}} in the Visco-Acoustic Vertical Transverse Isotropic Approximation},
  volume = {202},
  issn = {0956-540X},
  shorttitle = {Efficient 3-{{D}} Frequency-Domain Mono-Parameter Full-Waveform Inversion of Ocean-Bottom Cable Data},
  doi = {10.1093/gji/ggv226},
  abstract = {Abstract.  Computationally efficient 3-D frequency-domain full waveform inversion (FWI) is applied to ocean-bottom cable data from the Valhall oil field in the},
  language = {en},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Operto, S. and Miniussi, A. and Brossier, R. and Combe, L. and M\'etivier, L. and Monteiller, V. and Ribodetti, A. and Virieux, J.},
  month = aug,
  year = {2015},
  pages = {1362-1391},
  file = {/home/kazeiv/Zotero/storage/3V3WKM8I/Operto et al. - 2015 - Efficient 3-D frequency-domain mono-parameter full.pdf}
}

@article{sieminskiFinitefrequencySensitivitySurface2007,
  title = {Finite-Frequency Sensitivity of Surface Waves to Anisotropy Based upon Adjoint Methods},
  volume = {168},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2006.03261.x},
  abstract = {SUMMARY We calculate finite-frequency anisotropic traveltime sensitivity kernels for Rayleigh and Love waves using the recently developed combination of the adjoint method with spectral-element modelling of seismic wave propagation. We describe anisotropy following the ?natural? 13 elastic parameters for surface waves (A, C, F, L, N, Bc,s, Hc,s, Gc,s and Ec,s) complemented by eight ?body-wave parameters? (Jc,s, Kc,s, Mc,s and Dc,s). Along the ray path, the adjoint spectral-element computations agree well with asymptotic theory, but also expose the limitations of the asymptotic description. The adjoint spectral-element method is an efficient and flexible numerical tool, but it does not allow one to identify the various wave propagation phenomena contributing to the observed sensitivity. To decipher the numerical results, we apply Born scattering theory together with a surface-wave mode-coupling formulation. We identify a strong effect due to mode coupling. The sensitivity of Rayleigh waves for some of the anisotropic parameters is affected by Love?Rayleigh coupling, while Love-wave sensitivity is affected by cross-branch coupling. In addition, and very specific to anisotropy, the directional dependence of the sensitivity to azimuthal anisotropy may strongly distort the kernels, rendering them highly path-dependent. Because of these combined effects, the anisotropic sensitivity kernels can deviate substantially from the simple elliptical kernels used in recent isotropic finite-frequency tomography.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Sieminski, Anne and Liu, Qinya and Trampert, Jeannot and Tromp, Jeroen},
  month = mar,
  year = {2007},
  keywords = {Fréchet derivatives,adjoint methods,scattering,seismic anisotropy,sensitivity,surface waves},
  pages = {1153-1174},
  file = {/home/kazeiv/Zotero/storage/GAIDJIVG/Sieminski et al. - 2007 - Finite-frequency sensitivity of surface waves to a.pdf}
}

@article{sieminskiFinitefrequencySensitivityBody2007,
  title = {Finite-Frequency Sensitivity of Body Waves to Anisotropy Based upon Adjoint Methods},
  volume = {171},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.2007.03528.x},
  abstract = {We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by `banana\textendash{}doughnut' kernels which exhibit large, path-dependent variations and even sign changes. P-wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized `splitting intensity'. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver.},
  language = {en},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Sieminski, Anne and Liu, Qinya and Trampert, Jeannot and Tromp, Jeroen},
  year = {2007},
  keywords = {Fréchet derivatives,adjoint methods,seismic anisotropy,sensitivity,body waves,shear-wave splitting},
  pages = {368-389},
  file = {/home/kazeiv/Zotero/storage/V7EIP5BW/Sieminski et al. - 2007 - Finite-frequency sensitivity of body waves to anis.pdf}
}

@article{chenTheoreticalNumericalInvestigations2007,
  title = {Theoretical and Numerical Investigations of Global and Regional Seismic Wave Propagation in Weakly Anisotropic Earth Models},
  volume = {168},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2006.03218.x},
  abstract = {SUMMARY Smith and Dahlen demonstrated that in a weakly anisotropic earth model the relative surface wave phase-speed perturbation {$\delta$}c/c may be written in the form , where An and Bn are frequency-dependent depth integrals and ? denotes the ray azimuth. In this approximation, surface wave anisotropy is governed by 13 elastic parameters and the azimuthal dependence of the phase speed is represented by an even Fourier series in ? involving degrees zero (five elastic parameters), two (six elastic parameters), and four (two elastic parameters). Jech and Ps?enc?\'ik demonstrated that in such a weakly anisotropic earth model the relative compressional-wave phase-speed perturbation may be expressed as {$\delta$}c/c= (2c2)?1B33, whereas the relative shear wave phase-speed perturbations are given by {$\delta$}c/c= (4c2)?1\{B11+B22{$\pm$}[(B11?B22)2+ 4B212]1/2\}. We demonstrate that the coefficients B33, B11, B22, and B12 may be written in the generic form , where ? denotes the local azimuth and i the local angle of incidence. For B11, B22 and B33 the coefficients an(i) and bn(i) are an even Fourier series of degrees zero, two and four in i, but for B12 they are an odd Fourier series of degrees one and three. Like surface waves, the azimuthal (?) dependence of body waves involves even degrees zero (five elastic parameters), two (six elastic parameters), and four (two elastic parameters), but, unlike surface waves, it also involves the odd degrees one (six elastic parameters) and three (two elastic parameters). Thus, weakly anisotropic body-wave propagation involves all 21 independent elastic parameters. We use spectral-element simulations of global and regional seismic wave propagation to assess the validity of these asymptotic body and surface wave results. The numerical simulations and asymptotic predictions are in good agreement for anisotropy at the 5 per cent level.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Chen, Min and Tromp, Jeroen},
  month = mar,
  year = {2007},
  keywords = {surface waves,body waves,phase-speed perturbations,spectral-element simulations,weakly anisotropic earth model},
  pages = {1130-1152},
  file = {/home/kazeiv/Zotero/storage/FJ79XKWG/Chen and Tromp - 2007 - Theoretical and numerical investigations of global.pdf}
}

@article{berettaAVOAVAInversion2002,
  title = {{{AVO}} and {{AVA}} Inversion for Fractured Reservoir Characterization},
  volume = {67},
  issn = {0016-8033},
  doi = {10.1190/1.1451802},
  abstract = {Seismic wave reflection amplitudes are used to detect fluids and fracture properties in reservoirs. This paper studies the characterization of a vertically fractured fluid-filled reservoir by analyzing the reflection amplitudes of P-waves with varying incident and azimuthal angles. The reservoir is modeled as a horizontal transversely isotropic medium embedded in an isotropic background, and the linearized P-waves reflection coefficient are considered. The conditioning of the inverse problem is analyzed, and fracture density is found to be the best conditioned parameter. Using diffraction tomography under the Born approximation, an inversion procedure is proposed in the transformed k\textendash{$\omega$} domain to detect fracture density variations within the reservoir. Seismic data are rearranged in pairs of incident and reflected plane waves, enlightening only one spectral component of the fracture density field at a time. Only the observable spectral components are inverted. Moreover, working in the transformed domain, picking reflection amplitudes is not required. An example of the inversion applied to a synthetic data set is presented. The limitation of source and receiver numbers and the finite bandwidth of the wavelet produce a loss of resolution, but the overall fracture density variations are recovered correctly.},
  number = {1},
  journal = {GEOPHYSICS},
  author = {Beretta, M. and Bernasconi, G. and Drufuca, G.},
  month = jan,
  year = {2002},
  pages = {300-306},
  file = {/home/kazeiv/Zotero/storage/XQCD7IU2/Beretta et al. - 2002 - AVO and AVA inversion for fractured reservoir char.pdf}
}

@article{KazeiHeada,
  title = {P341 {{On}} the {{Contribution}} of {{Head Waves}} to {{Full Waveform Inversion}}},
  journal = {presented as poster P341 at the annual EAGE meeting in Copenhagen},
  author = {Kazei, Vladimir and Ponomarenko, A. V. and Troyan, V. N. and Kashtan, B. M. and Mulder, W. A.},
  year = {2012},
  publisher = {{EAGE}}
}

@article{KazeiHead,
  title = {On the {{Contribution}} of {{Head Waves}} to {{Full Waveform Inversion}}},
  author = {Kazei, Vladimir and Ponomarenko, A. V. and Troyan, V. N. and Kashtan, B. M. and Mulder, W. A.},
  year = {2012},
  howpublished = {74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012, Extended Abstracts, P341, Copenhagen, Denmark}
}

@inproceedings{kazeiCenteredDifferentialWaveform2017,
  title = {Centered {{Differential Waveform Inversion}} with {{Minimum Support Regularization}}},
  doi = {10.3997/2214-4609.201701336},
  abstract = {Time-lapse full-waveform inversion has two major challenges. The first one is the reconstruction of a reference model (baseline model for most of approaches). The second is inversion for the time-lapse changes in the parameters. Common model approach is utilizing the information contained in all available data sets to build a better reference model for time lapse inversion. Differential (Double-difference) waveform inversion allows to reduce the artifacts introduced into estimates of time-lapse parameter changes by imperfect inversion for the baseline-reference model. We propose centered differential waveform inversion (CDWI) which combines these two approaches in order to benefit from both of their features. We apply minimum support regularization commonly used with electromagnetic methods of geophysical exploration. We test the CDWI method on synthetic dataset with random noise and show that, with Minimum support regularization, it provides better resolution of velocity changes than with total variation and Tikhonov regularizations in time-lapse full-waveform inversion.},
  language = {English},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Kazei, Vladimir and Alkhalifah, T.},
  month = jun,
  year = {2017},
  file = {/home/kazeiv/Zotero/storage/BT26VAGR/Kazei and Alkhalifah - 2017 - Centered Differential Waveform Inversion with Mini.pdf}
}

@inproceedings{kazei2013spectral,
  title = {Spectral {{Sensitivity Analysis}} of {{FWI}} in a {{Constant}}-Gradient {{Background Velocity Model}}},
  doi = {10.3997/2214-4609.20130599},
  booktitle = {75th {{EAGE Conference}} \& {{Exhibition}} Incorporating {{SPE EUROPEC}} 2013},
  author = {Kazei, Vladimir and Kashtan, B. M. and Troyan, V. N. and Mulder, W. A.},
  year = {2013}
}

@book{voigtLehrbuchKristallphysikMit1910,
  title = {Lehrbuch Der Kristallphysik:(Mit Ausschluss Der Kristalloptik)},
  volume = {34},
  publisher = {{BG Teubner}},
  author = {Voigt, Woldemar},
  year = {1910}
}

@book{zotero-202,
  type = {Book}
}

@misc{PhysRev90,
  title = {Phys. {{Rev}}. {{B}} 90, 224104 (2014) - {{Necessary}} and Sufficient Elastic Stability Conditions in Various Crystal Systems},
  howpublished = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.224104}
}

@misc{LicensingMITVs,
  title = {Licensing - {{MIT}} vs {{GPL}} License},
  journal = {Stack Overflow},
  howpublished = {https://stackoverflow.com/questions/3902754/mit-vs-gpl-license}
}

@article{panEstimationElasticConstants2016,
  title = {Estimation of Elastic Constants for {{HTI}} Media Using {{Gauss}}-{{Newton}} and Full-{{Newton}} Multiparameter Full-Waveform Inversion},
  volume = {81},
  issn = {0016-8033},
  doi = {10.1190/geo2015-0594.1},
  abstract = {In seismic full-waveform inversion (FWI), subsurface parameters are estimated by iteratively minimizing the difference between the modeled and the observed data. We have considered the problem of estimating the elastic constants of a fractured medium using multiparameter FWI and modeling naturally fractured reservoirs as equivalent anisotropic media. Multiparameter FWI, although promising, remains exposed to a range of challenges, one being the parameter crosstalk problem resulting from the overlap of Fr\'echet derivative wavefields. Parameter crosstalk is strongly influenced by the form of the scattering pattern for each parameter. We have derived 3D radiation patterns associated with scattering from a range of elastic constants in general anisotropic media. Then, we developed scattering patterns specific to a horizontal transverse isotropic (HTI) medium to draw conclusions about parameter crosstalk in FWI. Bare gradients exhibit crosstalk, as well as artifacts caused by doubly scattered energy in the data residuals. The role of the multiparameter Gauss-Newton (GN) Hessian in suppressing parameter crosstalk is revealed. We have found that the second-order term in the multiparameter Hessian, which is associated with multiparameter second-order scattering effects, can be constructed with the adjoint-state technique. We have examined the analytic scattering patterns for HTI media with a 2D numerical example. We have examined the roles played by the first- and second-order terms in multiparameter Hessian to suppress parameter crosstalk and second-order scattering artifacts numerically. We have also compared the multiparameter GN and full-Newton methods as methods for determining the elastic constants in HTI media with a two-block-layer model.},
  number = {5},
  journal = {Geophysics},
  author = {Pan, W. and Innanen, K. and Margrave, G. and Fehler, M. and Fang, X. and Li, J.},
  month = jul,
  year = {2016},
  pages = {R275-R291},
  file = {/home/kazeiv/Zotero/storage/Y5YW2XSC/Pan et al_2016_Estimation of elastic constants for HTI media using Gauss-Newton and.pdf}
}

@incollection{kotsi4DFullwaveformMetropolis2018,
  series = {{{SEG Technical Program Expanded Abstracts}}},
  title = {{{4D}} Full-Waveform Metropolis Hastings Inversion Using a Local Acoustic Solver},
  abstract = {Time lapse seismic monitoring usually involves looking for small changes in localized regions. Quantifying the uncertainty related to these changes is important because it affects exploration and production decisions. Traditional methods that use pixel by pixel quantification with large models are computationally infeasible. We use a local acoustic solver in the area of interest, which allows for fast computation of the wavefield solves. This allows us to use a Metropolis Hastings algorithm in a Bayesian inversion to address the uncertainty that is present in the estimation of 4D velocity changes. Presentation Date: Tuesday, October 16, 2018 Start Time: 8:30:00 AM Location: 204C (Anaheim Convention Center) Presentation Type: Oral},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Kotsi, M. and Malcolm, A. and Ely, G.},
  month = aug,
  year = {2018},
  pages = {5323-5327},
  doi = {10.1190/segam2018-2997858.1}
}

@article{zhuLDMNetLowDimensional2017,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1711.06246},
  primaryClass = {cs},
  title = {{{LDMNet}}: {{Low Dimensional Manifold Regularized Neural Networks}}},
  shorttitle = {{{LDMNet}}},
  abstract = {Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-independent, and their efficacy is often limited when the training set is very small. Data-dependent regularizations are mostly motivated by the observation that data of interest lie close to a manifold, which is typically hard to parametrize explicitly and often requires human input of tangent vectors. These methods typically only focus on the geometry of the input data, and do not necessarily encourage the networks to produce geometrically meaningful features. To resolve this, we propose a new framework, the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features. In LDMNet, we regularize the network by encouraging the combination of the input data and the output features to sample a collection of low dimensional manifolds, which are searched efficiently without explicit parametrization. To achieve this, we directly use the manifold dimension as a regularization term in a variational functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami equation over a point cloud, which is solved by the point integral method without increasing the computational complexity. We demonstrate two benefits of LDMNet in the experiments. First, we show that LDMNet significantly outperforms widely-used network regularizers such as weight decay and DropOut. Second, we show that LDMNet can be designed to extract common features of an object imaged via different modalities, which proves to be very useful in real-world applications such as cross-spectral face recognition.},
  journal = {arXiv:1711.06246 [cs]},
  author = {Zhu, Wei and Qiu, Qiang and Huang, Jiaji and Calderbank, Robert and Sapiro, Guillermo and Daubechies, Ingrid},
  month = nov,
  year = {2017},
  keywords = {Computer Science - Computer Vision and Pattern Recognition},
  file = {/home/kazeiv/Zotero/storage/P65LZCFC/Zhu et al_2017_LDMNet.pdf}
}

@article{osypovModelUncertaintyQuantification2013,
  title = {Model-uncertainty Quantification in Seismic Tomography: Method and Applications},
  volume = {61},
  issn = {1365-2478},
  shorttitle = {Model-uncertainty Quantification in Seismic Tomography},
  doi = {10.1111/1365-2478.12058},
  language = {en},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Osypov, Konstantin and Yang, Yi and Fournier, Aim\'e and Ivanova, Natalia and Bachrach, Ran and Yarman, Can Evren and You, Yu and Nichols, Dave and Woodward, Marta},
  month = nov,
  year = {2013},
  pages = {1114-1134},
  file = {/home/kazeiv/Zotero/storage/YBDCY5BT/Osypov et al_2013_Model‐uncertainty quantification in seismic tomography.pdf}
}

@article{devaneyNonuniquenessInverseSource1982,
  title = {Nonuniqueness in Inverse Source and Scattering Problems},
  volume = {30},
  issn = {0018-926X},
  doi = {10.1109/TAP.1982.1142902},
  abstract = {The fields radiated by spherically symmetric time-harmonic sources are used to illustrate how little can be learned about a source from knowledge of the radiated field outside of the source volume. It is shown that even if it is known that the source is spherically symmetric, it is not possible to determine its radial structure. Moreover, even if the radial structure of the source is known apart from a constant amplitude and a finite radius, it is not possible to evaluate those two unknowns independently. These examples are applied to demonstrate explicitly that two methods that have been claimed to produce exact unique solutions to inverse-source and inverse-scattering problems do not yield the claimed results.},
  number = {5},
  journal = {IEEE Transactions on Antennas and Propagation},
  author = {Devaney, A. and Sherman, G.},
  month = sep,
  year = {1982},
  keywords = {Acoustic scattering,Antenna radiation patterns,Apertures,Current distribution,Electromagnetic scattering; inverse problem,H infinity control,Inverse scattering problem,Iterative methods,Magnetic resonance,Notice of Violation,Phased arrays,Sampling methods,Scattering},
  pages = {1034-1037},
  file = {/home/kazeiv/Zotero/storage/CAQZRR47/Devaney and Sherman - 1982 - Nonuniqueness in inverse source and scattering pro.pdf}
}

@article{SimultaneousNonlinearReconstruction,
  title = {Simultaneous Nonlinear Reconstruction of Two-Dimensional Permittivity and Conductivity},
  volume = {29},
  issn = {1944-799X},
  doi = {10.1029/93RS03448},
  abstract = {A new inversion algorithm for the simultaneous reconstruction of permittivity and conductivity recasts the nonlinear inversion as the solution of a coupled set of linear equations. The algorithm is iterative and proceeds through the minimization of two cost functions. At the initial step the data are matched through the reconstruction of the radiating or minimum norm scattering currents; subsequent steps refine the nonradiating scattering currents and the material properties inside the scatterer. Two types of basis functions are constructed for the nonradiating currents: ``invisible'' (global) basis functions, which are appropriate for discrete measurements and nonradiating (local) basis functions, which are useful in studying the limit of continuous measurements. Reconstructions of square cylinders from multiple source receiver measurements at a single frequency show that the method can handle large contrasts in material properties.},
  language = {en},
  number = {4},
  journal = {Radio Science},
  pages = {1101-1118},
  file = {/home/kazeiv/Zotero/storage/VH22U6CZ/Simultaneous nonlinear reconstruction of two-dimen.pdf}
}

@article{bergContrastSourceInversion1997,
  title = {A Contrast Source Inversion Method},
  volume = {13},
  issn = {0266-5611},
  doi = {10.1088/0266-5611/13/6/013},
  abstract = {This paper describes a simple algorithm for reconstructing the complex index of refraction of a bounded object immersed in a known background from a knowledge of how the object scatters known incident radiation. The method described here is versatile accommodating both spatially and frequency varying incident fields and allowing a priori information about the scatterer to be introduced in a simple fashion. Numerical results show that this new algorithm outperforms the modified gradient approach which until now has been one of the most effective reconstruction algorithms available.},
  language = {en},
  number = {6},
  journal = {Inverse Problems},
  author = {van den Berg, Peter M. and Kleinman, Ralph E.},
  year = {1997},
  pages = {1607},
  file = {/home/kazeiv/Zotero/storage/DAN8RZ64/Berg and Kleinman - 1997 - A contrast source inversion method.pdf}
}

@incollection{schusterApproximateInverseL2spaces2007,
  series = {Lecture {{Notes}} in {{Mathematics}}},
  title = {Approximate Inverse in {{L}}2-Spaces},
  isbn = {978-3-540-71226-8 978-3-540-71227-5},
  language = {en},
  booktitle = {The {{Method}} of {{Approximate Inverse}}: {{Theory}} and {{Applications}}},
  publisher = {{Springer, Berlin, Heidelberg}},
  author = {Schuster, Thomas},
  year = {2007},
  pages = {11-24},
  file = {/home/kazeiv/Zotero/storage/YKB5ERNY/Schuster - 2007 - Approximate inverse in Emphasis Type=ItalicL.pdf},
  doi = {10.1007/978-3-540-71227-5_2}
}

@article{bleisteinNonuniquenessInverseSource1977,
  title = {Nonuniqueness in the Inverse Source Problem in Acoustics and Electromagnetics},
  volume = {18},
  issn = {00222488},
  doi = {10.1063/1.523256},
  language = {en},
  number = {2},
  journal = {Journal of Mathematical Physics},
  author = {Bleistein, Norman and Cohen, Jack K.},
  year = {1977},
  pages = {194},
  file = {/home/kazeiv/Zotero/storage/DZ39PDG7/Bleistein and Cohen - 1977 - Nonuniqueness in the inverse source problem in aco.pdf}
}

@article{rudinNonlinearTotalVariation1992,
  title = {Nonlinear Total Variation Based Noise Removal Algorithms},
  volume = {60},
  issn = {0167-2789},
  doi = {10.1016/0167-2789(92)90242-F},
  abstract = {A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lanrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t {$\rightarrow$} {$\infty$} the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.},
  number = {1},
  journal = {Physica D: Nonlinear Phenomena},
  author = {Rudin, Leonid I. and Osher, Stanley and Fatemi, Emad},
  month = nov,
  year = {1992},
  pages = {259-268},
  file = {/home/kazeiv/Zotero/storage/H4P2SVN4/Rudin et al_1992_Nonlinear total variation based noise removal algorithms.pdf}
}

@article{fons2013,
  title = {Broadband Seismic Data ? {{The}} Importance of Low Frequencies},
  volume = {78},
  doi = {10.1190/geo2012-0294.1},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Ten Kroode, Fons and Bergler, Steffen and Corsten, Cees and {de Maag}, Jan Willem and Strijbos, Floris and Tijhof, Henk},
  year = {2013},
  pages = {WA3-WA14},
  eprint = {http://dx.doi.org/10.1190/geo2012-0294.1}
}

@article{kohnInfluenceModelParametrization2012,
  title = {On the Influence of Model Parametrization in Elastic Full Waveform Tomography},
  volume = {191},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2012.05633.x},
  abstract = {Elastic Full Waveform Tomography (FWT) aims to reduce the misfit between recorded and modelled data, to deduce a very detailed model of elastic material parameters in the underground. The choice of the elastic model parameters to be inverted affects the convergence and quality of the reconstructed subsurface model. Using the Cross-Triangle-Squares (CTS) model three elastic parametrizations, Lam\'e parameters m1 = [{$\lambda$}, {$\mu$}, {$\rho$}], seismic velocities m2 = [Vp, Vs, {$\rho$}] and seismic impedances m3 = [Ip, Is, {$\rho$}] for far-offset reflection seismic acquisition geometries with explosive point sources and free-surface condition are studied. In each CTS model the three elastic parameters are assigned to three different geometrical objects that are spatially separated. The results of the CTS model study reveal a strong requirement of a sequential frequency inversion from low to high frequencies to reconstruct the density model. Using only high-frequency data, cross-talk artefacts have an influence on the quantitative reconstruction of the material parameters, while for a sequential frequency inversion only structural artefacts, representing the boundaries of different model parameters, are present. During the inversion, the Lam\'e parameters, seismic velocities and impedances could be reconstructed well. However, using the Lam\'e parametrization -artefacts are present in the {$\lambda$} model, while similar artefacts are suppressed when using seismic velocities or impedances. The density inversion shows the largest ambiguity for all parametrizations. However, the artefacts are again more dominant, when using the Lam\'e parameters and suppressed for seismic velocity and impedance parametrization. The afore mentioned results are confirmed for a geologically more realistic modified Marmousi-II model. Using a conventional streamer acquisition geometry the P-velocity, S-velocity and density models of the subsurface were reconstructed successfully and are compared with the results of the Lam\'e parameter inversion.},
  language = {en},
  number = {1},
  journal = {Geophysical Journal International},
  author = {K\"ohn, D. and De Nil, D. and Kurzmann, A. and Przebindowska, A. and Bohlen, T.},
  month = oct,
  year = {2012},
  pages = {325-345},
  file = {/home/kazeiv/Zotero/storage/KU9Z3R3L/Köhn et al_2012_On the influence of model parametrization in elastic full waveform tomography.pdf}
}

@article{hoop1997,
  title = {Generalized {{Radon}} Transform Inversions for Reflectivity in Anisotropic Elastic Media},
  volume = {13},
  number = {3},
  journal = {Inverse problems},
  author = {De Hoop, Maarten V and Bleistein, Norman},
  year = {1997},
  pages = {669},
  publisher = {{IOP Publishing}}
}

@article{hoop1999,
  title = {The Resolving Power of Seismic Amplitude Data: {{An}} Anisotropic Inversion/Migration Approach},
  volume = {64},
  number = {3},
  journal = {Geophysics},
  author = {De Hoop, Maarten V and Spencer, Carl and Burridge, Robert},
  year = {1999},
  pages = {852-873},
  publisher = {{Society of Exploration Geophysicists}}
}

@inproceedings{blaseCharacterizationDentalTissue2018,
  title = {Characterization of Dental Tissue by Reflection and Transmission Ultrasound Microscopy},
  volume = {10600},
  doi = {10.1117/12.2300510},
  abstract = {Ultrasound (US) is a widely used modality for medical imaging, since it is non-invasive and relatively inexpensive. The ability of US imaging to detect internal structures, like tissue interfaces or lesion sites makes it a promising candidate for dental imaging. So far, the inherent technical difficulties of US imaging in tissues and organs with very heterogeneous (acoustic) properties and limited access have prevented its widespread use. In this study, we characterized the acoustic properties of sectioned teeth by scanning acoustic microscopy in reflection and transmission modes. The spatial distribution of sound velocity was measured in sections of extracted human teeth by use of a scanning acoustic microscope (SAM). Freshly extracted teeth were fixed in 4\% formaldehyde solution and embedded in a polymer block (PMMA). Sections of approximately 1 mm thickness were cut along the coronal-apical axis. Radio frequency (RF) data of teeth were collected in a scan region of 15 \&times; 15 mm\textsuperscript{2} by a SAM operating at 30 MHz with a lateral step size of 50 {$\mathrm{\mu}$}m and a sampling rate of 500 MSa/s. Sound velocity was determined from the time resolved reflection and transmission signals. Values for sound velocity from transmission mode were about 20\% lower than that from the reflection mode, if thickness information from reflection mode was used. If thickness was determined from the transmission mode, sound velocities from transmission were very close to those obtained from the reflection mode. Transmission mode is less sensitive to artifacts caused by the inclination of the specimen.},
  booktitle = {Health {{Monitoring}} of {{Structural}} and {{Biological Systems XII}}},
  publisher = {{International Society for Optics and Photonics}},
  author = {Blase, Christopher and Amjad, Umar and Kundu, Tribikram and {Bereiter-Hahn}, J\"urgen and Blume, Maximilian and Sader, Robert},
  month = mar,
  year = {2018},
  pages = {106000W},
  file = {/home/kazeiv/Zotero/storage/RJT43GIL/Blase et al_2018_Characterization of dental tissue by reflection and transmission ultrasound.pdf}
}

@article{vinnikObservationalEvidenceDiffracted1989,
  title = {Observational Evidence for Diffracted {{SV}} in the Shadow of the {{Earth}}'s Core},
  volume = {16},
  number = {6},
  journal = {Geophysical Research Letters},
  author = {Vinnik, Lev P. and Farra, Veronique and Romanowicz, Barbara},
  year = {1989},
  pages = {519-522}
}

@article{vinnikSeismicAnisotropyLayer1995,
  title = {Seismic Anisotropy in the {{D}} {${''}$}layer},
  volume = {22},
  number = {13},
  journal = {Geophysical Research Letters},
  author = {Vinnik, Lev and Romanowicz, Barbara and Le Stunff, Yves and Makeyeva, Larissa},
  year = {1995},
  pages = {1657-1660}
}

@article{boerConstructingDiscreteFracture2018,
  title = {Constructing a Discrete Fracture Network Constrained by Seismic Inversion Data},
  volume = {66},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12527},
  language = {en},
  number = {1},
  journal = {Geophysical Prospecting},
  author = {den Boer, Lennert D. and Sayers, Colin M.},
  month = jan,
  year = {2018},
  pages = {124-140},
  file = {/home/kazeiv/Zotero/storage/GU8N9K6U/Boer_Sayers_2018_Constructing a discrete fracture network constrained by seismic inversion data.pdf}
}

@article{ohOptimalFullWaveform2018,
  title = {Optimal Full Waveform Inversion Strategy for Marine Data in Azimuthally Rotated Elastic Orthorhombic Media},
  issn = {0016-8033},
  doi = {10.1190/geo2017-0762.1},
  abstract = {The orthorhombic anisotropic description of Earth layers can allow the capture many of the Earth's anisotropic complexity. The inversion for high-resolution azimuthal variation of anisotropy is important for reservoir characterization, among other applications. A high-resolution description of the azimuth of fractures can help us predict flow preferences. To verify the feasibility of multi-parameter full waveform inversion for marine data assuming azimuthally rotated elastic orthorhombic media, we analyze the radiation patterns and gradient directions of orthorhombic parameters to the reflection data. We first express the gradient direction of the orthorhombic parameters considering the azimuthal rotation of the symmetric planes. Then, to support our observations in the gradient direction, the radiation patterns of the partial derivative wavefields from each parameter perturbation are also derived under the rotated elastic orthorhombic assumption. To find an optimal parameterization, we compare three different parameterizations: monoclinic, velocity-based and hierarchical parameterizations. Then, we suggest an optimal multi-stage update strategy by analyzing the behavior of the rotation angle as an FWI target. To analyze the trade-off among parameters in different parameterizations, we calculate the gradient direction from a hockey puck model, in which each parameter is perturbed at the different location on a horizontal layer. The trade-off analysis supports that the hierarchical parameterization provides us with more opportunities to build up subsurface models with less trade-off between parameters and less influence of the azimuthal rotation of orthorhombic anisotropy. The feasibility of the proposed FWI strategy is examined using synthetic marine streamer data from a simple 3D reservoir model with a fractured layer.},
  journal = {GEOPHYSICS},
  author = {Oh, J. and Alkhalifah, T.},
  month = mar,
  year = {2018},
  pages = {1-61},
  file = {/home/kazeiv/Zotero/storage/5D9YUJDZ/Oh_Alkhalifah_2018_Optimal full waveform inversion strategy for marine data in azimuthally rotated.pdf}
}

@article{chang3D3CFullwavefield2009,
  title = {{{3D}} 3-{{C}} Full-Wavefield Elastic Inversion for Estimating Anisotropic Parameters: {{A}} Feasibility Study with Synthetic Data},
  volume = {74},
  issn = {0016-8033},
  shorttitle = {{{3D}} 3-{{C}} Full-Wavefield Elastic Inversion for Estimating Anisotropic Parameters},
  doi = {10.1190/1.3204766},
  abstract = {Traveltime-based inversions cannot solve for all of the anisotropy parameters for orthorhombic media. Vertical velocities cannot be recovered simultaneously with the dimensionless anisotropy parameters. Also, the density cannot be solved because it does not affect the normal moveout of P and S reflections. These limitations can be overcome using full-wavefield inversion for anisotropy parameters for orthorhombic media and for transversely isotropic media with vertical and horizontal symmetry axes. Tsvankin's parameters and the orientation of the local (anisotropic) coordinates are inverted from three-component, wide-azimuth data sets containing P reflected and PS converted waves. The inversions are performed in two steps. The first step uses only reflections from the top of an anisotropic layer, whichdoes not constrain the trade-offs between the vertical velocities, the anisotropies, and density, as shown by parameter correlation analysis. The results from the first step are refined by using them as the starting model for the second step, which fits reflections from the top and bottom of the layer. The properties of the target layer influence the amplitudes of top and bottom reflections as well as the traveltime of the bottom reflections; when all these data are used, the inversion is highly overdetermined and all model parameters are estimated accurately. When Gaussian noise is added, the inversion results are very similar to those for the noise-free data because only the coherent signal is fitted. The residual at convergence for the noisy data corresponds to the noise level. Concurrent inversion of data from multiple sources increases the azimuthal illumination of a target.},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Chang, H. and McMechan, G.},
  month = nov,
  year = {2009},
  pages = {WCC159-WCC175},
  file = {/home/kazeiv/Zotero/storage/FFIARNEE/Chang_McMechan_2009_3D 3-C full-wavefield elastic inversion for estimating anisotropic parameters.pdf}
}

@inproceedings{ohOptimalFullWaveform2017,
  title = {Optimal {{Full Waveform Inversion Strategy}} in {{Azimuthally Rotated Elastic Orthorhombic Media}}},
  doi = {10.3997/2214-4609.201701232},
  abstract = {The elastic orthorhombic assumption is one of the most practical Earth models that takes into account the horizontal anisotropic layering and vertical fracture network. In this model, the rotation angle of the vertical planes of symmetry is a crucial parameter needed to increase the convergence of an anisotropic full waveform inversion (FWI) as well as to provide the fracture geometry along azimuthal direction. As an initial step, we investigate the possibility of recovering the azimuth angle via FWI, which may offer high-resolution information. We first utilize our new parameterization with deviation parameters, which provides the opportunity for multi-stage FWI. Based on the radiation patterns and gradient directions of each parameter, we show that the azimuth angle mainly affects the parameters that have azimuth-dependent radiation patterns, so that we can hierarchically build up the subsurface model from isotropic to VTI to azimuthally rotated orthorhombic models with less trade-offs. From the numerical example for a synthetic 3D model, we expect that both a deviation parameter and the azimuth angle can be recovered in the last stage of FWI with minimum trade-offs.},
  language = {English},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Oh, J. W. and Alkhalifah, T.},
  month = jun,
  year = {2017},
  file = {/home/kazeiv/Zotero/storage/EVQVJD4K/Oh_Alkhalifah_2017_Optimal Full Waveform Inversion Strategy in Azimuthally Rotated Elastic.pdf}
}

@inproceedings{routhFullWavefieldInversion2012,
  series = {{{SEG Technical Program Expanded Abstracts}}},
  title = {Full {{Wavefield Inversion}} of {{Time}}-{{Lapse Data}} for {{Improved Imaging}} and {{Reservoir Characterization}}},
  abstract = {We apply full wavefield inversion (FWI) to determine from time-lapse data the changes in the subsurface due to production. It is well recognized that a significant velocity change between the baseline and monitor survey introduces a time shift in the seismic data. Current practices are to apply time-shift analysis or to perform time-shift inversion to interpret such changes. These changes can be large enough that the background velocity model needs to be updated between the base and the monitor survey. Ideally if the velocity models can be estimated for both the base and monitor surveys, then these large changes can be interpreted. The FWI framework is ideally suited to accomplish this task. The objective of this paper is to demonstrate this concept and its impact on imaging time-lapse data. A synthetic 2D example is used to demonstrate the solution to this problem.},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2012},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Routh, P. and Palacharla, G. and Chikichev, I. and Lazaratos, S.},
  month = sep,
  year = {2012},
  pages = {1-6},
  doi = {10.1190/segam2012-1043.1}
}

@article{zuberiMitigatingNonlinearityFull2018,
  title = {Mitigating Nonlinearity in Full Waveform Inversion Using Scaled-{{Sobolev}} Pre-Conditioning},
  volume = {213},
  issn = {0956-540X},
  doi = {10.1093/gji/ggx549},
  abstract = {The Born approximation successfully linearizes seismic full waveform inversion if the background velocity is sufficiently accurate. When the background velocity is not known it can be estimated by using model scale separation methods. A frequently used technique is to separate the spatial scales of the model according to the scattering angles present in the data, by using either first- or second-order terms in the Born series. For example, the well-known `banana-donut' and the `rabbit ear' shaped kernels are, respectively, the first- and second-order Born terms in which at least one of the scattering events is associated with a large angle. Whichever term of the Born series is used, all such methods suffer from errors in the starting velocity model because all terms in the Born series assume that the background Green's function is known. An alternative approach to Born-based scale separation is to work in the model domain, for example, by Gaussian smoothing of the update vectors, or some other approach for separation by model wavenumbers. However such model domain methods are usually based on a strict separation in which only the low-wavenumber updates are retained. This implies that the scattered information in the data is not taken into account. This can lead to the inversion being trapped in a false (local) minimum when sharp features are updated incorrectly. In this study we propose a scaled-Sobolev pre-conditioning (SSP) of the updates to achieve a constrained scale separation in the model domain. The SSP is obtained by introducing a scaled Sobolev inner product (SSIP) into the measure of the gradient of the objective function with respect to the model parameters. This modified measure seeks reductions in the L2 norm of the spatial derivatives of the gradient without changing the objective function. The SSP does not rely on the Born prediction of scale based on scattering angles, and requires negligible extra computational cost per iteration. Synthetic examples from the Marmousi model show that the constrained scale separation using SSP is able to keep the background updates in the zone of attraction of the global minimum, in spite of using a poor starting model in which conventional methods fail.},
  language = {en},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Zuberi, M. Ah and Pratt, R. G.},
  month = apr,
  year = {2018},
  pages = {706-725},
  file = {/home/kazeiv/Zotero/storage/E7UFW6HS/Zuberi_Pratt_2018_Mitigating nonlinearity in full waveform inversion using scaled-Sobolev.pdf}
}

@article{choi2012,
  title = {Application of Multi-source Waveform Inversion to Marine Streamer Data Using the Global Correlation Norm},
  volume = {60},
  issn = {0016-8025},
  doi = {10.1111/j.1365-2478.2012.01079.x},
  abstract = {ABSTRACT Conventional multi?source waveform inversion using an objective function based on the least?square misfit cannot be applied to marine streamer acquisition data because of inconsistent acquisition geometries between observed and modelled data. To apply the multi?source waveform inversion to marine streamer data, we use the global correlation between observed and modelled data as an alternative objective function. The new residual seismogram derived from the global correlation norm attenuates modelled data not supported by the configuration of observed data and thus, can be applied to multi?source waveform inversion of marine streamer data. We also show that the global correlation norm is theoretically the same as the least?square norm of the normalized wavefield. To efficiently calculate the gradient, our method employs a back?propagation algorithm similar to reverse?time migration based on the adjoint?state of the wave equation. In numerical examples, the multi?source waveform inversion using the global correlation norm results in better inversion results for marine streamer acquisition data than the conventional approach.},
  number = {4},
  journal = {Geophysical Prospecting},
  author = {Choi, Yunseok and Alkhalifah, Tariq},
  month = jun,
  year = {2012},
  keywords = {Global correlation,Marine streamer data,Modelled},
  pages = {748-758},
  file = {/home/kazeiv/Zotero/storage/FLF79QSI/Choi Yunseok_Alkhalifah Tariq_2012_Application of multi‐source waveform inversion to marine streamer data using.pdf}
}

@article{wuSimultaneousInversionBackground2015,
  title = {Simultaneous Inversion of the Background Velocity and the Perturbation in Full-Waveform Inversion},
  volume = {80},
  issn = {0016-8033},
  doi = {10.1190/geo2014-0365.1},
  abstract = {The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeling, to fit the observed data. When the initial velocity was smooth, the data modeled from the source using the background velocity will mainly be reflection free, and most of the reflections were obtained from the image (perturbed velocity). As the background velocity becomes more accurate and can produce reflections, the role of the image will slowly diminish, and the update will be dominated by the standard FWI gradient to obtain high resolution. Because the objective function was quadratic with respect to the image, the inversion for the image was fast. To update the background velocity smoothly, we have combined different components of the gradient linearly through solving a small optimization problem. Application to the Marmousi model found that this method converged starting with a linearly increasing velocity, and with data free of frequencies below 4~Hz. Application to the 2014 Chevron Gulf of Mexico imaging challenge data set demonstrated the potential of the proposed method.},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Wu, Z. and Alkhalifah, T.},
  month = sep,
  year = {2015},
  pages = {R317-R329},
  file = {/home/kazeiv/Zotero/storage/4EHNR4MS/Wu_Alkhalifah_2015_Simultaneous inversion of the background velocity and the perturbation in.pdf}
}

@article{hermans2016,
  title = {Covariance-Constrained Difference Inversion of Time-Lapse Electrical Resistivity Tomography Data},
  volume = {81},
  doi = {10.1190/geo2015-0491.1},
  number = {5},
  journal = {GEOPHYSICS},
  author = {Hermans, Thomas and Kemna, Andreas and Nguyen, Fr\'ed\'eric},
  year = {2016},
  pages = {E311-E322},
  eprint = {http://dx.doi.org/10.1190/geo2015-0491.1}
}

@article{zhang2012,
  title = {A Regularized Three-Dimensional Magnetotelluric Inversion with a Minimum Gradient Support Constraint},
  volume = {189},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Zhang, Luolei and Koyama, Takao and Utada, Hisashi and Yu, Peng and Wang, Jialin},
  year = {2012},
  pages = {296-316},
  publisher = {{Oxford University Press}}
}

@article{blaschek2008,
  title = {A New Sensitivity-Controlled Focusing Regularization Scheme for the Inversion of Induced Polarization Data Based on the Minimum Gradient Support},
  volume = {73},
  number = {2},
  journal = {Geophysics},
  author = {Blaschek, R and H\"ordt, A and Kemna, A},
  year = {2008},
  pages = {F45-F54},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{zhdanov1999,
  title = {Focusing Geophysical Inversion Images},
  volume = {64},
  doi = {10.1190/1.1444596},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Portniaguine, Oleg and Zhdanov, Michael S.},
  year = {1999},
  pages = {874-887},
  eprint = {http://dx.doi.org/10.1190/1.1444596}
}

@inproceedings{denli2009,
  title = {Double-Difference Elastic Waveform Tomography in the Time Domain},
  booktitle = {2009 {{SEG Annual Meeting}}},
  author = {Denli, Huseyin and Huang, Lianjie and others},
  year = {2009},
  organization = {{Society of Exploration Geophysicists}}
}

@article{asnaashari2015,
  title = {Time-Lapse Seismic Imaging Using Regularized Full-Waveform Inversion with a Prior Model: Which Strategy?},
  volume = {63},
  number = {1},
  journal = {Geophysical prospecting},
  author = {Asnaashari, Amir and Brossier, Romain and Garambois, St\'ephane and Audebert, Fran{\c c}ois and Thore, Pierre and Virieux, Jean},
  year = {2015},
  pages = {78-98}
}

@inproceedings{watanabe2004,
  title = {Differential Waveform Tomography for Time-Lapse Crosswell Seismic Data with Application to Gas Hydrate Production Monitoring},
  booktitle = {2004 {{SEG Annual Meeting}}},
  author = {Watanabe, Toshiki and Shimizu, Shoshiro and Asakawa, Eiichi and Matsuoka, Toshifumi and others},
  year = {2004},
  organization = {{Society of Exploration Geophysicists}}
}

@article{hicks2016,
  title = {Time-Lapse Full-Waveform Inversion as a Reservoir-Monitoring Tool \textemdash{}- {{A North Sea}} Case Study},
  volume = {35},
  number = {10},
  journal = {The Leading Edge},
  author = {Hicks, Erik and Hoeber, Henning and Houbiers, Marianne and Lescoffit, S\'everine Pannetier and Ratcliffe, Andrew and Vinje, Vetle},
  year = {2016},
  pages = {850-858},
  publisher = {{Society of Exploration Geophysicists}}
}

@inproceedings{felixes2015,
  title = {Using Common Information in Compressive Time-Lapse Full-Waveform Inversion},
  booktitle = {77th {{EAGE Conference}} and {{Exhibition}} 2015},
  author = {Oghenekohwo, Felix and Kumar, Rajiv and Esser, Ernie and Herrmann, Felix J},
  year = {2015}
}

@article{zhdanov2002,
  title = {Geophysical Inverse Theory and Regularization Problems},
  author = {Zhdanov, M S},
  year = {2002},
  publisher = {{Elsevier}}
}

@article{maharramov2016,
  title = {Time-Lapse Inverse Theory with Applications},
  volume = {81},
  number = {6},
  journal = {Geophysics},
  author = {Maharramov, Musa and Biondi, Biondo L and Meadows, Mark A},
  year = {2016},
  pages = {R485-R501},
  publisher = {{Society of Exploration Geophysicists}}
}

@inproceedings{reparametrized2016,
  title = {Joint Reparametrized Time-Lapse Full-Waveform Inversion},
  doi = {10.1190/segam2016-13879371.1},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2016},
  author = {Alemie, Wubshet and Sacchi, Mauricio},
  year = {2016},
  pages = {1309-1314},
  eprint = {http://library.seg.org/doi/pdf/10.1190/segam2016-13879371.1}
}

@article{surTotalVariationMinimization2015,
  title = {Total Variation Minimization for Spectrum Interpolation in Quasiperiodic Noise Removal},
  journal = {https://members.loria.fr/FSur/software/ACARPENOS/note\_TVmin.pdf},
  author = {Sur, Frederic},
  year = {2015},
  pages = {6},
  file = {/home/kazeiv/Zotero/storage/KC7JA6CB/Sur - Total variation minimization for spectrum interpol.pdf;/home/kazeiv/Zotero/storage/LWCNQI54/Sur - Total variation minimization for spectrum interpol.pdf}
}

@inproceedings{kurzmann2016,
  address = {Cham},
  title = {Seismic {{Applications}} of {{Full Waveform Inversion}}},
  isbn = {978-3-319-47066-5},
  abstract = {Full waveform inversion (FWI) is a powerful imaging technique which exploits the richness of seismic waveforms. We further developed FWI to obtain multi-parameter images at high resolution. Here, we involve physical parameters, such as velocities and attenuation of seismic waves as well as mass density, which are essential for a reliable petrophysical characterization of subsurface structures in hydrocarbon exploration, geotechnical applications and underground constructions. Referring to this, we successfully applied FWI to field datasets recorded in the Black Sea and in the shallow-water area of a river delta in the Atlantic Ocean. We obtained detailed subsurface images containing rock formations which might be potential gas deposits. Additionally, we performed synthetic studies as preparatory steps to verify methodological improvements for further field-data applications. Here, we demonstrate resolution capabilities of FWI for imaging geological structures beneath salt bodies, investigate strategies to recover attenuation information from seismic data and perform a joint inversion of surface waves to image the very shallow subsurface.},
  booktitle = {High {{Performance Computing}} in {{Science}} and {{Engineering}} 16},
  publisher = {{Springer International Publishing}},
  author = {Kurzmann, A. and Ga\ss{}ner, L. and Thiel, N. and Kunert, M. and Shigapov, R. and Wittkamp, F. and Bohlen, T. and Metz, T.},
  editor = {Nagel, Wolfgang E. and Kr\"oner, Dietmar H. and Resch, Michael M.},
  year = {2016},
  pages = {647-665}
}

@book{claerbout1985fundamentals,
	title={Fundamentals of geophysical data processing},
	author={Claerbout, Jon F},
	year={1985},
	publisher={Blackwell scientific publications}
}

@book{claerbout1985,
  title = {Imaging the {{Earth}}'s {{Interior}}},
  abstract = {@book\{claerbout1985imaging,
  title=\{Imaging the earth's interior\},
  author=\{Claerbout, Jon F\},
  volume=\{1\},
  year=\{1985\},
  publisher=\{Blackwell scientific publications Oxford\}
\}},
  publisher = {{Blackwell scientific publications}},
  author = {Claerbout, Jon F},
  year = {1985},
  file = {/home/kazeiv/Zotero/storage/RBLKRXYN/Claerbout - Imaging the Earth's Interior.pdf}
}

@book{zotero-246,
  type = {Book}
}

@article{xuAnellipticApproximationGeometric2018,
  title = {An Anelliptic Approximation for Geometric Spreading in Transversely Isotropic and Orthorhombic Media},
  volume = {83},
  issn = {0016-8033, 1942-2156},
  doi = {10.1190/geo2017-0038.1},
  language = {en},
  number = {1},
  journal = {GEOPHYSICS},
  author = {Xu, Shibo and Stovas, Alexey and Sripanich, Yanadet},
  month = jan,
  year = {2018},
  pages = {C37-C47},
  file = {/home/kazeiv/Zotero/storage/WJNKS3Y7/Xu et al. - 2018 - An anelliptic approximation for geometric spreadin.pdf}
}

@article{xuNewParameterizationAcoustic2017,
  title = {A New Parameterization for Acoustic Orthorhombic Media},
  volume = {82},
  issn = {0016-8033, 1942-2156},
  doi = {10.1190/geo2017-0215.1},
  abstract = {We have defined a group of new parameterizations for P-wave in acoustic orthorhombic (ORT) media with three cross-term normal moveout velocities and three cross-term anellipticity parameters. The corresponding perturbationbased approximations for traveltime in ORT model are developed using the new parameterizations. The perturbation coefficients are computed by solving the eikonal equation in corresponding parameterization. Eight types of parameterization are defined based on the different elliptical background model and selection of anellipticity parameters. As the traveltime can be converted from the group velocity inverse, the sensitivity of the group velocity inverse to anellipticity parameters is analyzed for different parameterizations and different range of offsets. To stabilize the perturbation series and improve the accuracy, the Shanks transform is applied. From the comparison of traveltime after the Shanks transform using different parameterizations, we have concluded that the parameterization with vertical, two horizontal velocities, and three cross-term anellipticity parameters results in the best accuracy of traveltime function for P-wave in acoustic ORT medium.},
  language = {en},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Xu, Shibo and Stovas, Alexey},
  month = nov,
  year = {2017},
  pages = {C229-C240},
  file = {/home/kazeiv/Zotero/storage/AI4KRY2C/Xu and Stovas - 2017 - A new parameterization for acoustic orthorhombic m.pdf}
}

@article{stovasAzimuthallyDependentKinematic2015,
  title = {Azimuthally Dependent Kinematic Properties of Orthorhombic Media},
  volume = {80},
  issn = {0016-8033, 1942-2156},
  doi = {10.1190/geo2015-0288.1},
  abstract = {An orthorhombic velocity model covers anisotropy and vertical/horizontal heterogeneity in the uniform 3D framework. It is important to define the azimuthal dependence of kinematic parameters of this model in the phase and group domains. I have derived equations for azimuthal dependent anellipticity in orthorhombic media and a simple equation to link the group and phase azimuths at zero horizontal slowness projection (zero offset). I found that the orthorhombic media cannot be treated as azimuthally dependent transversely isotropic media. To define the effective kinematic properties from a multilayered orthorhombic medium is a nontrivial task, and I have developed an approximate leastsquares solution for that problem. Numerical examples with the orthorhombic model and its special cases (a transversely isotropic model with vertical and horizontal symmetry axes and an elliptical isotropic model) were used to illustrate the effect of the individual orientation of symmetry planes on the effective kinematic properties.},
  language = {en},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Stovas, Alexey},
  month = nov,
  year = {2015},
  pages = {C107-C122},
  file = {/home/kazeiv/Zotero/storage/XP7UTAXI/Stovas - 2015 - Azimuthally dependent kinematic properties of orth.pdf}
}

@article{schoenbergOrthorhombicMediaModeling1997,
  title = {Orthorhombic Media: {{Modeling}} Elastic Wave Behavior in a Vertically Fractured Earth},
  volume = {62},
  issn = {0016-8033, 1942-2156},
  shorttitle = {Orthorhombic Media},
  doi = {10.1190/1.1444297},
  abstract = {Vertical fractures and horizontal fine layering combine to form a long-wavelength equivalent orthorhombic medium. Such media constitute a subset of the set of all orthorhombic media. Orthorhombic elastic symmetry is the lowest symmetry for which the slowness surface (the solution of the Christoffel equation) is bicubic rather than sextic. Various properties of orthorhombic media, such as the number and location of conical points and longitudinal directions, may be derived from the slowness surface or, because of its bicubic character, the squared slowness surface, which is a cubic surface. From the occurrence and angular orientation of some of these distinctive features, conclusions can be drawn with respect to the properties of the medium and to the parameters of the assumed underlying causes of the anisotropy. The estimation of these more subtle properties gains greater importance with the proliferation of multiazimuthal seismic surveys and the ability to drill along ever-more complicated 3-D well trajectories.},
  language = {en},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Schoenberg, Michael and Helbig, Klaus},
  month = nov,
  year = {1997},
  pages = {1954-1974},
  file = {/home/kazeiv/Zotero/storage/QE8KC4VV/Schoenberg and Helbig - 1997 - Orthorhombic media Modeling elastic wave behavior.pdf}
}

@article{prieuxMultiparameterFullWaveform2013,
  title = {Multiparameter Full Waveform Inversion of Multicomponent Ocean-Bottom-Cable Data from the {{Valhall}} Field. {{Part}} 2: Imaging Compressive-Wave and Shear-Wave Velocities},
  volume = {194},
  issn = {0956-540X},
  shorttitle = {Multiparameter Full Waveform Inversion of Multicomponent Ocean-Bottom-Cable Data from the {{Valhall}} Field. {{Part}} 2},
  doi = {10.1093/gji/ggt178},
  abstract = {Multiparameter elastic full waveform inversion (FWI) is a promising technology that allows inferences to be made on rock and fluid properties, which thus narrows the gap between seismic imaging and reservoir characterization. Here, we assess the feasibility of 2-D vertical transverse isotropic visco-elastic FWI of wide-aperture multicomponent ocean-bottom-cable data from the Valhall oil field. A key issue is to design a suitable hierarchical data-driven and model-driven FWI workflow, the aim of which is to reduce the nonlinearity of the FWI. This nonlinearity partly arises because the shear (S) wavespeed can have a limited influence on seismic data in marine environments. In a preliminary stage, visco-acoustic FWI of the hydrophone component is performed to build a compressional (P)-wave velocity model, a density model and a quality-factor model, which provide the necessary background models for the subsequent elastic inversion. During the elastic FWI, the P and S wavespeeds are jointly updated in two steps. First, the hydrophone data are inverted to mainly update the long-to-intermediate wavelengths of the S wavespeeds from the amplitude-versus-offset variations of the P\textendash{}P reflections. This S-wave velocity model is used as an improved starting model for the subsequent inversion of the better-resolving data recorded by the geophones. During these two steps, the P-wave velocity model is marginally updated, which supports the relevance of the visco-acoustic FWI results. Through seismic modelling, we show that the resulting visco-elastic model allows several P-to-S converted phases recorded on the horizontal-geophone component to be matched. Several elastic quantities, such as the Poisson ratio, and the ratio and product between the P and S wavespeeds, are inferred from the P-wave and S-wave velocity models. These attributes provide hints for the interpretation of an accumulation of gas below lithological barriers.},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Prieux, Vincent and Brossier, Romain and Operto, St\'ephane and Virieux, Jean},
  month = sep,
  year = {2013},
  pages = {1665-1681},
  file = {/home/kazeiv/Zotero/storage/LDH9QHR2/Prieux et al_2013_Multiparameter full waveform inversion of multicomponent ocean-bottom-cable.pdf}
}

@article{brossierSeismicImagingComplex2009,
  title = {Seismic Imaging of Complex Onshore Structures by {{2D}} Elastic Frequency-Domain Full-Waveform Inversion},
  volume = {74},
  issn = {0016-8033},
  doi = {10.1190/1.3215771},
  abstract = {Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Brossier, R. and Operto, S. and Virieux, J.},
  month = nov,
  year = {2009},
  pages = {WCC105-WCC118},
  file = {/home/kazeiv/Zotero/storage/FMQX73NH/Brossier et al_2009_Seismic imaging of complex onshore structures by 2D elastic frequency-domain.pdf}
}

@inproceedings{vegard2017,
  title = {Parameter Resolution and Cross-Talk for {{Elastic Full Wavefrom Inversion}}},
  volume = {19},
  abstract = {Elastic Full Waveform Inversion (EFWI) is a computationally intensive method for iteratively estimating elastic subsurface model parameters. A cornerstone of EFWI is the numerical solution of the elastic wave equation, which is used as a tool to quantify the discrepancy between the synthetic (modelled) and true (real) measured seismic data at the receiver locations. The difference between the modelled and real recorded data is subsequently used to update the synthetic model to yield a better match between the modelled and true receiver data. A common approach to the EFWI problem is to use a non-linear conjugate gradient search method for the updates. The resolution and
cross-coupling for the estimated parameters can then be found by computing the Hessian matrix. For application to exploration seismic data, resolution of the estimated model parameters depend on the chosen parametrisation, acquisition geometry and temporal frequency range. Although some experience has been gained, it is still not clear which elastic parameters can be reliably estimated. Previous analyses, with some exception, have been based on simplistic arguments using radiation pattern analysis. We use a known adjoint-state technique to compute the Hessian for realistic exploration cases and analyse parameter resolution and cross-coupling for different selections of models, acquisition geometries and data types, including streamer and Ocean Bottom Seismic recordings. The information on resolution obtained from the exact Hessian is essential for evaluating the quality of estimated parameters due to the strong influence of source-receiver geometry and frequency content. For typical exploration type models and acquisition parameters unbiased estimates of pressure- and shear wave velocities can be obtained, but density appears to be coupled strongly to other
parameters.},
  booktitle = {{{EGU General Assembly Conference Abstracts}}},
  author = {Stenhjem Hagen, Vegard and Arntsen, B\o{}rge},
  month = apr,
  year = {2017},
  pages = {7013},
  file = {/home/kazeiv/Zotero/storage/UVGJTME5/Stenhjem Hagen_Arntsen_2017_Parameter resolution and cross-talk for Elastic Full Wavefrom Inversion.pdf}
}


